Cannot get Apple mail to accept passwords for Gmail on MacPro
I am running 10.13.3 on a mid-2012 Mac Pro. I cannot get Apple Mail to accept any passwords for Gmail. I have no issue with my iPad, iPhone or on the web. I do not have 2-step verification turned on with any of my devices or with Gmail. Yesterday, for a few hours, mail was working, then it was back to endless attempts to enter passwords for my two Gmail accounts. I should point out that I was having the same problem with my iCloud account but that mysteriously started working and is still working. I have tried to add a Proton Mail account with the same results as the Gmail accounts. Both Gmail accounts are configured to be IMAP.
I have owned dozens of Macs through the years starting with the Mac Plus but since my extended warranty has run out on this machine, no one at Apple will talk to me. I "think" that the problem began with the 10.13.3 update but that belies the fact that both were working for a while yesterday.
Please, someone put me out of my misery with a good answer.