Like you, I have the '87 300TD. Mine works the way you described with left and right indicators away from the curb . . .

I believe fuses #3 & #8, both 8 amp, are within the circuit. As I have read several times, worth double-checking them just to get that issue out of the way. From there, probably a test light within the socket with your switch in the correct position and key out of the ignition. That last is probably not necessary yet I have always checked mine in the state they are designed to work in (car parked and locked). From viewing the schematic, it shouldn't make any difference since there should be power always available. Keep us posted with your findings.
Steve

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Steve
'87 300TD - 132K - Soon 4-Sale
'84 300D Turbo - 122K - Driving
'77 VW Type II - 77K - Restored
'08 250EX Ninja
English Bulldog (Brier) - My best friend. Passed away 12/02/04 while in my arms.