I alway wonder why all these passive inquiries about validity. Just ask the priest when and who ordained them. For most priests that was the most significant and meaningful day of their life…most enjoy talking about their vocation and ordination…not to mention, it helps you get to know the person your going to entrust your immortal soul to.
Courage my friend, courage! Strap on some courage and go talk to your priest!
Sometimes you can't even get their contact information, and they just show up at your chapel, so then you're scrambling to figure out whether they're undoubedtly valid priests. I've been in that situation many times, where you're pulling up your web browser after Father "Smith" shows up at your friendly neighborhood SSPX chapel one weekend.
Best you can do is to see if you can find mention of their ordination online. Good luck figuring out where they're stationed so that you even have a phone number to call. Last "Priest Assignments" web page on their site hasn't been updated since 2018.
In addition, some priests will get hostile if you don't ask the question the "right way", usually obliquely, "Hi, Father, were you at STAS? When it was at Winona or Virginia?" That's a good first question. But the minute some get the impression that your'e asking, "Are you conditionally ordained?", they'll immediately label you a closet sedevacantist or closet Resistance, which could compromise your position at the chapel.
This is all due to the SSPX playing footsie with the Modernists.