I agree - start with the flasher itself.

It doesn't hurt to have a basic understanding of how the flasher in a domestic classic car works - it's simply a low capacity circuit breaker. The load of lighting the turn signal bulbs heats it up, causing it to open the circuit. Once the circuit is open (without load), things cool down, and the breaker closes again. Repeat.

Your symptoms sound like a mix. Things other than a haywire flasher sort of go like this:

a. Flashes very slow or not at all: Insufficient load on the circuit. Often simply a bulb burned out.

b. Flashes faster than normal: Higher load on the circuit than expected. Dirty, higher resitance socket. Perhaps a vandal connected a trailer (with its additional lights) without your knowledge.