Adding power off to existing amps

I picked up a Pass Labs X1 pre-amplifier and it has a 12 VDC "Amp Turn On" output signal. The manual specifies it handles 50mA max. Has anyone found a way to use this signal to turn on/off the external amplifiers that don't have this feature? I was thinking to insert a relay to close the power switch in the amps when activated. Alternatively, I could avoid modifying the amps and build switched outlets. I have two questions to ask:
  1. Is doing this a bad idea?
  2. What relays and/or circuit should I use?
    The relays I found either don't provide any current specifications on the DC input at all or their rating is too high (~48mA per relay).
Thanks.
 
To answer your questions:
  1. No, it can be done.
  2. This depends on the power supply circuit of the amplifier. Some amplifiers can be turned on through a switched outlet, while some amplifiers have built-in standby circuits and still need to press the power button on the front panel to activate.
What is your amplifier?
 
I have a Threshold s/200 and a Sanders Audio Crossover Amp. The latter is pretty much the same as the s/200 as it was designed at CODA by previous Threshold designers. The former lends itself to the switched outlet as it only has a master power switch. The latter can't or it resets the configuration. However it has a dedicated amplifier power switch that does this. I'm more interested in the s/200 as it runs hot while idle, the Sanders doesn't.
 
Ready made unit for 120VAC mains:

1722884050948.jpeg

https://cdn.sparkfun.com/assets/a/5/d/a/f/iot2spec.pdf

https://www.digikey.com/en/products/detail/scs/770069/13152231?