Toad turn signal lights don't blink when tail lights are on.

I've have a 2000 Coachmen Class C motor home on a Ford E-450 cutaway chassis. I tow a 2004 Honda CRV behind it with a Blue OX towbar. I have a problem with the extra lights on the toad. If the coach's tail lights are on, the turn signal lights barely blink, the just stay bright with a very slight dimming each cycle instead of turning off and on. I have the same problem whether I use magnetic tow lights or additional lights I wired into the CRV tail lights. If the running lights/tail lights are off, the lights blink correctly. I've replaced the blinker relay with a heavy duty one with no difference. Looking for ideas how to isolate and fix the problem.
Thanks!