For First Generation Mustang, Cougar, Falcon 9and likely more) when the Upper Control Arm Bushing(s) begin to dry out they will cause a squeaking sound when going over bumps. The sound can be replicated, if that is the cause, by simply pushing down on one of the front fenders and letting the front suspension spring puch the fender back up. If you determine the Upper Control Arm Bushings are causing the sound the "fix" is to install some Zerk grease fittings into the two ends of the Upper Control Arm Bushing mounting shaft, then pushing grease into the bushings using a regular grease gun. If you are lucky there will already be some Zerk fittings, with a 90 degree turn, installed. Otherwise you will need to remove the two mounting shaft end plugs (already threaded for Zerk fittings), and install the Zerk fittings.
The bad news is there is very little distance between the Upper Control Arm Shaft ends and the shock tower metal. But, there some more good news. The clearance between the Upper Control Arm Mounting Shaft ends and the Shock Tower metal is a little larger for 1971 - 1973, as opposed to earlier year Mustang, Falcon, Cougar vehicles. So, installing a Zerk fitting at both ends of the mounting shaft is not terribly difficult. Further, there is a kit available with not only the Zerk fittings, but a special, very flat Zerk fitting/plug wrench that will help make installing a Zerk fitting be an easy task.
Please download and look at the attached Shop Manual snippet that covers suspension repair procedures. Refer to pages 1, 19, 21, and 22 for details.
I also have a YouYube video that shows where the Zerk fitting are located, and how they are lubricated at:
https://www.youtube.com/watch?v=X2kgHn-XhVc
I hope that helps you with the squeaking sound you are getting.