Dick was a good man.... in fact I bought one of his X's a few years back (Deadwood Special, for my youngest son, when he graduated from Hi school). And when he passed, his wife offered the bike you have to me. Lucky you!! Congrats!!
With our X's aging.... and there appears to be quite a few that just sit, my first guess, is that the injectors got plugged up. It isn't uncommon, and I've worked on a couple of X's with injector problems already from sitting around...
Being I don't know your wrenching skills, but I'll suggest you contact Bobby Baldwin at the "Biker Shack" in Alpine Calf. ... as he does still work on X's when they show up. Bobby isn't listed as a vendor on this site... but he's in your same state... close enough, and he knows X's very well. Your next closest would be Charlie Brandon, and he's listed on this site as a vendor.
Otherwise, its really not that tough of a job. Pretty sure all of the vendors on this site have injectors, and a few have rebuilts. Also another option, if you look around here on the www, you'll notice that our injectors are the same ones that the fuelie Triumphs use. So if you have a local Triumph dealer theres another option.
I highly recommend that you pull that tank, and fuel pump.... and get it cleaned up inside there, otherwise the problem will persist and haunt you. And if you can afford it, maybe have that tank resealed.
get cornered.... give out a shout!
Bruce