The House merely indicts...the trial occurs in the Senate.
Correct. Since impeachment = indictment, if the person is indicted, by definition the “impeachment” works. It is the Senate’s responsibility to convict or not convict, but that does not annul, repeal or nullify the House’s duty to indict. If they refuse to do their duty, they are complicit with all the high crimes and misdemeanors that they refuse to indict.
Once the person is impeached, it is the Senate who will have to look at the evidence and vote. Based on that evidence and their votes, we can know which senators are complicit and need to be removed and which care about this country.