You mean connect the white wire where the yellow wire is, and the yellow where the white is?

White wire at its proper connection provides power that operates the relay coil and the blinker lights themselves.

So connecting the yellow wire, which brings no power, to that place results in no lights at all. No coil, no lights. The white wire, which has power, connects to a inside contact that is a dead end unless the coil operates.

You might find a replacement relay at AutoZone or a similar place.

Good Luck,

Bob

:>)