I think Trey Anastasio is a fairly strict alternate picker, so we can find a lot of examples of how the concept can be applied in Phish songs. I’ll get to some more eventually, but for starters, I thought the little intro lick to “Stash” would be a good example. In the process, you can also get some practice on a diminished arpeggio.
The lick is mostly made up of 8th notes, but has a couple of rests, and a couple of notes that fall on the upstroke and get some extra emphasis. Best bet is to take a look at the video to see a demonstration. Here’s a tab of the lick in question: