One of those pull switch types? Those contain the park, turn signal cross circuit, and the emergency flash on.... the fourth pull click? The lever for the turn signals complete by closing contacts and as mentioned to heat a bimetal turn signal relay element that when heated opens, breaks contact with bulbs, cools then closes again to re light the bulbs. The turn lever brakes the connection ultimately.
Turn signal is possible as the 555 timer in this quick fix would be in a slow pulsing mode at all times.
Thoughts are if the 4 way emergency also uses the same relay for all lights to flash, this would work IF the control switch functions that way (uses the same relay for both turn and emergency).
The 555 timer would pulse at a low on, off, and the timer would function a P-Channel (to drive the lamps as they are often chassis grounded at their location for reduced production cost) to power the lamps dictated (control) determining what row, left/right to be linked via the turn signal lever.
.... The Timer should be left ON, IF the 4 way emergencies are tied into the same relay and are not working as well, why? If the ignition switch is off and the timer would be off as well, the emergency would not work with the ignition off if you wanted the ignition switch to control the 555 timers power. The emergency would tie the P-channel to all lamps at activation of Emergency switch. (Running the 555 timer at all times may beBad for battery if left on for a long period, don't know the battery, tho this is a quick fix, temporary) ?
: Edited the bad for battery remark :
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So 555 Timer slow constant pulsing set by the time you want (looks authentic OE blinking) , a P-Channel that can carry the total lamp current (all) with some current head room left for transistor to drive the lamps, or parallel transistor arrangement, P-Channel driving the to the lamps connector from the relays port, and the main turn signal lever controlling left or right as usual. BJT, current Base to switch on/ documentation, FET, follow documentation of that part for Gate voltage. This is a likely sourcing operation of power to the lamps.
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The other relays port should have a constant power regardless, I'm assuming a 2 pin relay with a positive supply from battery? Careful, those relay ports for the flasher lamps may not be fused from the battery to work in event of vehicle damage unless the battery is defunct. (not likely)