From your description the electric motor brushes sound like they are nearly worn out. But, the convertible top motor is not something I would expect to have been used so much that the brushes would have worn out "already," as compared to brushes in the alternator or starter motor - even the windshield wiper motor or windshield washer motor. But, these are complex machines, and anything is possible. Before chasing down a new motor I think it is worth looking at the entire circuitry for the power top system.
Attached is a snippet from the 1973 Mustang schematic I have, with a correction (actually, one of several minor corrections throughout the master schematic file). The schematic shows Fuse #2 is used for the convertible top switch, but that is not what is really going on. Yep, that's right, the schematic is wrong when they cover the Fuse Block section in the schematic (page 1 of the PDF snippet file).
I have annotated the schematic file that is attached to this comment to reflect how the circuit is really set up. As mentioned elsewhere in this thread, there is a circuit breaker coming off the positive cable terminal side of the Starter Relay that feeds the convertible top switch directly. The Circuit Breaker feeds Circuit 175 (Black with Yellow Dot) that then feeds the convertible top switch directly (no relays), and provides power for the optional engine compartment light's mercury on/off switch. No relay for the convertible top is shown in the schematics, and I have never seen a relay for one. The relays I have seen in the 71-73 Mustangs are for the seat back latch actuators (solenoids), the starter, power back-lite, headlight on warning, and power windows. See the right lower section of Page 1 of the file named "1973Mustang_ConvertibleTopCircuitry_20220123.pdf" attached to this message. I hope the schematic helps you out.
I find a lot of intermittent and unusual behaviors are caused by loose or poor grounds. There is a Ground #803 in the schematic, which is shown in both of the last two pages of schematic drawings, but on the last page of the schematic diagrams are drawn details are given re: where Ground #803 is located, along with 3 connector locations and connector drawings (lower right quadrant of the last schematic page in the attached file). I have highlighted those areas with a red box outlining them. Every one of those connections, and the ground, need to be checked before trying to locate a switch and/or motor for replacement, in my humble opinion.
To make things even more complicated, another enthusiast reported to me his convertible top stopped working until he replaced Fuse #4. I recorded that having been reported in the next-to-the-last page in the attached PDF file, but can't make any sense of why that might have happened as Fuse #4 controls no circuits related to the convertible top (see top left of Page 1, and schematic grid location B31 in the attached file). But, I recorded it anyway in case there is a variant wiring not included in the schematic files I have. I am thinking this Car Season I am going to pull Fuse #4 in our 73 Mustang Convertible to see if it impacts our convertible top power or not. I am both betting, and hoping, it does not impact it.
