What should Republican senators do now?

Mostly they want to talk about something else.

Those senators will be remembered about as fondly as their predecessors who weren't sure about the 13th Amendment. Or are they going to remembered like Margaret Chase Smith or like Robert Taft?

It doesn't take a great constitutional scholar to figure this out. How would they have reacted if Obama had done any of these things? It didn't take much to get the Republicans into a frenzy about Bill Clinton.

But it's time to put aside politics for a while and practice conscientious statesmanship. Conscientious statesmen Republican senators might consider a five step plan -

Urge Trump to be fully and consistently presidential for the rest of his time in office, whether it's five years or five days. Presidential for all the people, not just his base, not imperial, not mafiosish. No more obstruction, and appoint one and only one attorney to discuss all impeachment issues - the man who represents himself has a fool for a client and a fool for an attorney. The president is having none of it.
If there really is no case against Trump, then it won't hurt to provide all the witnesses and documents the Democrats want. Urge Trump to devote his time to making progress on workable issues like drug prices, background checks on gun purchases, and infrastructure - bills that the House has passed and the Senate has refused to consider. That way, when the Senate trial reaches the point of voting for or against conviction and removal, a Republican senator has a defensible basis for voting against.
If Trump won't or can't, then -
Urge Trump to resign in return for a full pardon from President Pence. The pardon not because Trump deserves it, but because the country deserves to get past Trump as soon as possible. Note that a presidential pardon does not apply to state or civil matters.
If Trump won't, then -
Urge Pence to invoke the 25th Amendment, again with a full pardon for Trump is he goes along promptly and quietly.
If Pence won't or can't, then -
Urge the House Democrats to bring forward an impeachment resolution as quickly as possible, so the Senate can act on it quickly and senators can move on to building a case for their own re-election. Whether the Senate convicts and removes or not, Republican senators are going to have to do a lot of explaining to do, either in the next primary or the next general election. They should plan to do this early and often so they get good at it, because if all the previous plans fail, they can count on Trump generating new impeachable offenses and Putin making the most of them and new articles of impeachment from the House - practically on a daily basis.
So when it comes to voting on Trump's conviction and removal, perhaps Republican senators should just vote "present." That way they can say they didn't vote to remove Trump, or they can say that they didn't vote to exonerate Trump, whichever seems to be more advantageous in days to come. Nobody will be surprised if they say the one thing on odd days and the opposite on even days, to cover all their bases.
As for pardons, Trump should consider that whenever his term ends he can expect the same sort of vindictive prosecution that he inflicts on his foes. If he is succeeded by a Democrat he won't get any pardon except the self-pardon he drafts himself on his last day in office. Whether that self-pardon is binding would certainly be decided by the Supreme Court. They might run down the clock for him but they might decide quickly. These uncertainties might be best avoided by a timely resignation coupled with a pardon from Pence. Of course, a presidential pardon extends only to Federal crimes and not to state crimes or civil matters.
But when all is said and done -
Republicans don't have to renominate Trump or Pence.
And even if Trump were convicted and removed in the Senate - the Republicans could still nominate him again for 2020. Nothing in the Constitution prevents that - his base would turn out in force, which wouldn't be enough for him to win - but that turnout would help Republican candidates down ballot, except of course for the Republican senators who had voted to impeach and convict, who then had managed to survive their primaries. And re-nominating Trump would spare the Republicans the possibility of their worst nightmare, that he would run out of spite, as a third-party candidate or an independent, and thus assure the triumph of whomever the Democrats nominate, even if it be Hillary Clinton again.

If Pence had become president sooner, then the Republicans would still have gotten all the tax cuts and deregulation and reactionary Federal judges that their donors expect. And they might even have retained control of the House. That opportunity has passed, but perhaps the Republicans could keep control of the Senate in 2020 if voters had a year to forget about former President Trump. Electoral projections from 2018 to 2020 do not look good for Trumpists in swing districts.

The polls are shifting, but not-yet-former President Trump is making it clear what's in store for Republicans who cross him. How they wish they could vote in secret in the House and in the Senate.

A few are trying to lead the way out, including Colin Powell and George Conway. Will any senators follow them?

Cracks are beginning to show. Reactionary politicians might not buy into herd immunity when it comes to vaccinations, but they definitely believe in it for hard political choices. If they decide against Trump in favor of Pence, it will go from just a few senators one day to almost all of them the next day. Nobody wants to be first or second, but they don't want to be last, either. Self-serving opportunists, whether in the White House or Congress, are always on the lookout for a better opportunity. They owe Trump no more loyalty than he would show them.

The worst choice would be for a few Republicans to wait for the election to support a third-party or independent candidate. If they drew enough independent swing voters - they'd guarantee Trump's re-election.

Would President Pence be a tolerable alternative?.

Hanging over all of this is the inevitable recession that follows every recovery. Too bad for Republicans if it becomes apparent before the election and they are still standing with Trump. If the Republican senators stand together and remove Trump in time, they can blame the recession on him if it arrives later at an inconvenient moment.

Shouldn't there be a less painful process for getting rid of an incompetent president? Why not replace the impeachment process and the 25th amendment process with something simple: the House may nominate a new president at any time for any reason, by 2/3 vote if the office is occupied, majority vote if the office is vacant; the nominee is sworn in unless the Senate vetoes the nomination by 2/3 vote with 3 days if the Senate is in session, 7 days otherwise. The same mechanism could replace the Electoral College as well.