So I just got the mustang running pretty good after an engine swap and now my airbag light is blinking whenever its running. The car has been sitting for 4+ years and I don't know where to start. 

This one has been covered a few times on the forums but start by figuring out what the code means.
Mustang 1995 Air Bag Diagnostic Codes
I did the following to my Xterra, worked for it. Caveat...this is for an Xterra, don't know if it will work on a Mustang, but just offering it to you to try it out, takes 30 seconds and its free. I'm sure Nissan and Ford software engineers are two different animals but hey... Maybe it'll work out. Good luck!
1. Turn the key from off to on.
2. Watch the airbag light closely. It will stay on for a few secs. and then as soon as it blinks off (the start of the flashing), turn the key off instantly.
3. Count to 5 (1 Mississippi, 2 Mississippi . . . .)
4. Repeat steps 1-3 two more times until you have done the cycle three times.
5. Now turn the key on and watch the light. It will start blinking in a different, slower manner. This is diagnostic mode. You can watch this for a little while, no hurry.
6. Now turn the key off again, Count to 5 like in step 3 again, and turn back on. If the procedure worked, the airbag light will not be flashing.