Did you test the TPS with the engine running ..... or KOEO? The TPS is supposed to read just a hair over 1 volt with the engine running, and just a hair under with KOEO. But if 1.20V is the lowest you could get .... you're right, you should probably replace it.
I don't know about any special tools reguired, but I could be wrong. The only thing I can think of that would be helpful is a press .... or something of the like .... to press the gear off. Here, I'll just post up an article of where a guy change out his ignition module & stator at the same time. (note: he refers to the ignition control module as a TFI IV .... as he's doing this on a Fox. Also, the module on his car is located at the distributor. Ours is not.)
EDIT: this is all here to help you IF you do not want to just replace the whole distributor/stator. Some would just replace the whole thing just to avoid the hassle of putting the new stator in. Whatever you want to do, though.
I have had intermittent ignition symptoms on my 87 Mustang GT for quite a while, and they occurred infrequently enough that meaningful troubleshooting-by-symptom was nearly impossible. When I did have a
problem, the following symptoms were present: 95% of my problems were a failure to start, and 5% were occasional engine stalls or bucking while driving. The tachometer read 0 during an event. Turning the key off for 30 second before retrying would often get me going. Normally, no EEC-IV error codes were present, but over a 6-month period I did get one code 14 = "Erratic Ignition". Eventually, I found the source of my problem in the distributor, which is MUCH cheaper than the EEC-IV processor unit. The distributor has only one moving part, unlike the olden days of points and centrifugal or vacuum advance, so it REALLY is more reliable!
There are two replaceable electronic components in the distributor. (1) The TFI-IV (Thick Film Integrated) module, sometimes called a modulator, is the grey plastic part on the side of the distributor body. (2) The
Hall-effect sensor, also known as the stator or pickoff, mounts internally. To be conservative, Ford recommends replacing both the TFI-IV and stator as a set, so that's what I did, but I suspect my stator was OK. OEM list prices are about $100 for the TFI module, and $50 for the stator. Third-party vendor prices are about 30-45% less. It's likely that the design of the TFI-IV has been improved, so installing an older (used) one may not effect a long-term fix.
The distributor MUST be removed from the vehicle to replace the stator, and most probably the TFI-IV module as well. It's really no big deal. Don't forget to clean the area at the base of the distributor before removing it. Label and disconnect cylinders 1-4 from the cap and move it aside. Note the PRECISE position of both the distributor housing and the rotor for reassembly later. You'll also need a 5.5mm or 7/32" nut driver. I had to grind down the O.D. of mine to fit into the recess on the TFI-IV module. Don't forget the heat sink compound when you install a new one. Replacing the stator is a LOT more work, as you must completely disassemble the distributor. You'll have to drive out the roll pin and press the camshaft-driven gear off the distributor shaft, which is a hassle if you don't have a hydraulic press, but can still be done with a hammer if you're careful and creative. Don't forget to note the orientation of the gear on the shaft. Removal of the shaft retaining collar is much simpler than the gear because it's not a press fit. In my case, the 100K-mile engine had
gum & varnish deposits on the exposed portions of the distributor shaft which made removal from the distributor body more difficult. I inverted the distributor in a vise and poured some solvent into the base, then spun
the shaft with an electric drill while gently working it back and forth until it slid free. When reassembling, be VERY careful to align the gear on the shaft before pressing it back into place, or you'll have to press it
off and retry.
If you reinstalled everything carefully, you should be within a few degrees of proper timing. Warm up the engine, remove the SPOUT connector plug from the harness near the distributor and set the timing to 10 degrees BTDC. Reinsert the SPOUT jumper and you're back on the road with confidence!