Do you have a TM wait list?

Yes, I do.
...but as a solo player, with no gyms in range to tell me about raids, I don't really have a chance to get any, so it is pointless.
I could drive around and use petrol in hope that I stumble on a raid worth doing, and hope it has players there to help - but it would be more fuel efficient to join these snipers who use maps....at least I will know I actually get a chance to throw a ball at something if I bother to drive all the way there.

My game consists of going around and earning lots coins for other players on rival teams.

This game has become so much fun now...

Right now, I really want only one charge TM for my B/FB Tyranitar. But RNG refuses to grant me that. I have yet to get one (after 84 raids).

If I can ever get that one, then I'll try for more less pressing ones:

My 100% Dragonite with DB/HB. I want O but will gladly take H.
My other Dragonite with DT/HB. I really want O on that one.
Then, if I ever have extra charge TMs, I might give my KC/Sub Machamp a roll and hope for DP. But since HS is a huge risk (and based on my past luck with RNG is what I'll get), I'll wait until I have a few in my bag.

Flareon e/ft>fs/ft
Scizor bp/xs>fc/xs
Gyarados b/dp>b/hp
Have already used 8 tms on dragonite hb, tyrannitar fb, vaporeon wg, exeguttor seb, golem ms and a few others.
In hindsight the Tm on tyrannitar wasnt really necessary as i caught 5 in raids

Flareon only. I quit after it learns Overheat.

I'd keep Crunch on your Gyarados.
For Mewtwo, with Focus Blast.
You might think of changing him into B/C instead...

I guess just Rhydon at this point. I have RS/SE and RS/EQ, but apparently (with your list) those are good moves? I'm wondering if I should go for MS/SE//EQ :/

I was lucky enough to pick up 11 TMs (4, 7) in the first week, but none since. I used one on a SW Dragonite and another on a Machamp. I'm holding on to the others for now, but am considering:
L35 vaporeon with WP
L33 Eggy with C/Seed Bomb
L30 Alakazam with Shadow Ball
L35 Jolteon with Thunder
L36 Blissey with Psychic
L37.5 Dragonite with DPulse

Hit that Flareon up if he's a good level already maybe.

The rest are iffy personal choices you'd need to talk me into. None are automatic.

Side note NEVER change 5. please

Seems like you've been out of the loop for a while. Some of those movesets that you want aren't the best anymore in the current meta - especially with raids.

Based on your list, I would personally do the following:
For Boss Raid, Rhydon is your priority to use TM. Rhydon MS/EQ would be very useful for Boss raid. Lanturn is good if it has gd CP/IV. Exeggutor w/ (C/SoB) is apparently a gd defending moveset, since the change of gym meta, no one really care of holding the gym for too long so if I need to I would prefer to have BS/SB for grass type boss battle
For Attack, Gyarados w/ (DT/OR) against Dragonite, Dophan w/ (C/PR) against Fight/Dark/Dragon type. These 2 mons has high CP capacity which r worth investing.
As for the rest... just leave it as it is

I got two fast TMs and one charge TM. These went to Tyranitar IT/C -> B/C, Tyranitar IT/SE -> B/SE, and dragonite DB/Hb -> DB/O. This was my initial TM priority list. I since caught a B/C Tyranitar in a raid with better IVs than the one I TMed. The only difference is 66 candies and 70,000 dust already spent on the TMed one.

If and when, I get more TMs, I am considering, Dragonite SW/HB -> DT/{H,O}; Otherwise, mu impression is that TMs are very rare, and I should wait for Unobtainable -> Awful Move/Awful Move -> great move/great move, but don't have a specific candidate in mind. Other stuff, I will continue to grind for the old fashioned way.

If someday, I am rolling in TMs, I'll be more casual about using them.

I have this 65% lv30 Tyranitar that I evolved from a Larvitar but spent no dust on. Got the classic IT/FB too. I couldn't bring myself to transfer it. A buddy suggested TMing it. At first I said are you crazy its got bad IVs but then i realized I would literally never use it except maybe against an ice mon. So I TMd it and now have B/C. I might use this guy now!

I only have 1 TM (fast) and I think I will use it in my SW/O Dragonite to get DT.
Next on my list are:
Flareon E/OH to FS/OH
Rhydon RS/SE to MS/SE (I already have several with MS/SE but this one is 100% so I may use a TM just to have the best moveset)
Espeon C/psybeam to C/FS

Charge:
98% B/Tw Gyarados
93% Sw/HB Dragonite
Quick:
93% RS/Eq Rhydon
Possibly the Gary and Dragonite above depending on the new charge move.