Let me see if I can help:
The FCC won't issue new three-letter calls, period. Under certain circumstances, it will sometimes allow a station that once had a three-letter call to regain the use of that call. If you were to buy 1260 or 93.3 in San Francisco, you'd have a shot at persuading the FCC to let you revert to "KYA." Any other station? Almost certainly not.
As for four-letter calls, once they've been changed, they go back into the pool of available callsigns and can once again be requested by anyone, so long as nobody's using the base callsign. It doesn't matter whether the user of the base callsign has an -FM or -TV suffix or not, it's in their control as to whether anyone else can use that base callsign in another service. So because Audacy has KFRC in use in San Francisco on the FM band, anyone who wanted to use KFRC on AM or TV somewhere else would have to try to get Audacy's permission (and probably wouldn't get it).
As long as you give the correct legal ID (callsign, city of license, with a handful of optional insertions in between) once an hour, the FCC doesn't care what you call yourself the rest of the hour. Note that listeners to KFRC on 106.9 hear nothing but "KCBS" all hour except for the legal ID. You could call your station "KYA" all hour long if you wanted (and I think you'll find there have been several stations over the years that have done just what you're contemplating as homages to the original KYA.)
But...
Everything I've said so far is from the FCC's perspective. There are no "trademarks" at the FCC. Trademarks are a completely separate area of commercial law, and I am not a lawyer, so this is a very basic non-expert overview: a business can register a trademark at either the state level (in which case it applies only in that state) or at the federal level (in which case it applies nationwide). Trademarks last for only a limited time, and only if they remain in active use.
If you wanted to use old imaging elements, logos, and such, you also need to consider copyright law. The jingle companies were pretty good about copyrighting their material and there's a non-zero chance you could get into trouble for using that material in a commercial context, even half a century later.
The FCC won't issue new three-letter calls, period. Under certain circumstances, it will sometimes allow a station that once had a three-letter call to regain the use of that call. If you were to buy 1260 or 93.3 in San Francisco, you'd have a shot at persuading the FCC to let you revert to "KYA." Any other station? Almost certainly not.
As for four-letter calls, once they've been changed, they go back into the pool of available callsigns and can once again be requested by anyone, so long as nobody's using the base callsign. It doesn't matter whether the user of the base callsign has an -FM or -TV suffix or not, it's in their control as to whether anyone else can use that base callsign in another service. So because Audacy has KFRC in use in San Francisco on the FM band, anyone who wanted to use KFRC on AM or TV somewhere else would have to try to get Audacy's permission (and probably wouldn't get it).
As long as you give the correct legal ID (callsign, city of license, with a handful of optional insertions in between) once an hour, the FCC doesn't care what you call yourself the rest of the hour. Note that listeners to KFRC on 106.9 hear nothing but "KCBS" all hour except for the legal ID. You could call your station "KYA" all hour long if you wanted (and I think you'll find there have been several stations over the years that have done just what you're contemplating as homages to the original KYA.)
But...
Everything I've said so far is from the FCC's perspective. There are no "trademarks" at the FCC. Trademarks are a completely separate area of commercial law, and I am not a lawyer, so this is a very basic non-expert overview: a business can register a trademark at either the state level (in which case it applies only in that state) or at the federal level (in which case it applies nationwide). Trademarks last for only a limited time, and only if they remain in active use.
If you wanted to use old imaging elements, logos, and such, you also need to consider copyright law. The jingle companies were pretty good about copyrighting their material and there's a non-zero chance you could get into trouble for using that material in a commercial context, even half a century later.