Check your starter solenoid. I recently had a similar problem with my 1989 f-150. What ended up being the problem was the connection from the ignition switch to the solenoid (see image below).Make sure that is a secure connection, without any corrosion, dirt, or debris. This connector should pull straight off with some resistance. If the connection is sloppy loose (happens over time), then take a pair of needle nose pliers (or an equivalent), and squeeze down the connector just a little bit so that it has an oblong (oval) shape to it.
DON'T OVERDUE IT. It only needs enough to keep it holding itself securely in place.Hope this helps, If this is not the problem, I'm pretty great with fixing older ford trucks. Reply back to me if this is not the problem.