For 1992, so I can't be entirely sure that yours will be the same. There, it indicates Code 34 is "Low resistance in driver air bag circuit." To me, this may indicate a clockspring problem, or perhaps a short somewhere else in the wiring to the driver's airbag?
I also feel like I've read in the past about a "shorting pin" that is integral to the air-bag connectors, designed to short out the connector for safety when you unplug it. Could the driver's air bag simply be disconnected? I've researched these systems, but never had to troubleshoot one. It may be a place to start.
After a bit more digging, the same website has a 1995 code reference, also. (http://www.veryuseful.com/mustang/tech/airBag/airBag95.html) The Code 34 on that list, is "Driver Side Air Bag Circuit Low Resistance or Shorted" Similar, but adds the possibility that it could be shorted. Regardless, I suspect you're looking at the driver's side bag.
If the code is intermittent, check the front crash sensors for good ground contact. They should each be retained by a single bolt to the front header panel. Unbolt them, thoroughly clean the mounting surfaces of any rust or corrosion and replace. It would also be wise to check the ground wire connection(s) to the header panel.