I owned a 71 Comet and the side markers 'blinked' when signals were applied. Side markers used a single filament bulb.
They do this by connecting one lead of the bulb to the running light and the other lead to the turn signal switch.
Side lights operate normally when running lights are on but turn off as the flasher can opens up the circuit when signals are applied.
This gives the impression that they are flashing when in effect they are just turning off and on.
The disclaimer is, I don't know if this can be used on a trailer.
Schematic is from a 72 Maverick.