69 Valiant - Electrical / Turn Signal Question

I’m new to this so bare with me.

I have a 1969 Plymouth Valiant. Currently, I am experiencing issues with my passenger side blinker / brake light. It does not work when I engage the turn signal switch / brake. The parking light works fine. I understand that the blinker / brake lights are on the same circuit so if I locate the source of the problem, both issues should be corrected. The issue only pertains to the right hand (passenger) side. The left hand (drivers) side functions as it should. Here are my questions:

1 – People say "double check your fuse", but if the fuse was blown, wouldn’t the left hand (drivers) side not function? I wouldn’t think that each side would be powered separately.

2
– Regarding the flasher relay: If the flasher relay was bad, wouldn’t the symptoms be the same when trying to signal either direction? When I apply the left directional, you get it all,.. the external blinker, the clicking noise and flash indicator on the cluster (brake light works as well). When I signal right I get nothing. No flash indicator on the cluster (stuck on or otherwise), and no clicking (no brake light as well).

Obviously I am going to have to make sure that all of my connections are good, and that I have good ground to the rear tail light assembly, but it’s the lack of clicking noise / flash indicator illumination on the cluster that leads me to believe my turn signal switch might not be making contact as it should when trying to signal right.

What do you think?
Any info you might have would be very much appreciated.