I have a 1991 Honda Accord that started experiencing some electrical issues yesterday. At first, the right turn signal would not turn off. Shortly after, the turn signals stopped working completely but the hazard signals still work. Any idea which of the relays or fuses I should suspect?
Some cars have a separate flasher relay for the Hazards - if that's the case then you might have a failure of the primary flasher relay?
The signal initially not turning off suggests a possible failure of the switch though - It might be worth disconnecting the switch (there's usually a connection somewhere under the column) and testing it separately? I'm not sure about Hondas, but some cars of that age were known for the lighting stalk failing as they didn't have relayed headlamps, so the full current of the headlamp flowed through the switches - leading to failure as they get old!
For cases where the culprit is not the switch, it could be the flasher relay in cars that have separate indicator flasher and hazard flasher relays. (Which is common for example in oldtimer cars and trucks that originally had no hazard flasher at all and then got an aftermarket one added after years.)
How to check for a faulty flasher relay. To test if the relay is the problem, you can take it out and insert a wire bridge between input (pin 49) and output (pin 49a) instead. This is just a permanent connection where the flasher relay will create an intermittent "flashing" connection when operating, so it will not damage anything. Now when operating the indicator switch and it makes the indicator lights of one side light up (without the flashing), the relay is at fault. Otherwise, it could be the switch or fuses.
(Pin names are Geman DIN 72 551 ones. They would be X or B for the flasher relay input and L for the output in USA and UK – source.)