Check for current leakage in the areas around the on/off switch.
Some decades ago I had a Macintosh II which had a habit of turning
itself on without human intervention - usually in the morning.
I eventually traced the problem to the keyboard. The Mac II uses a
"soft" power switching setup, where the keyboard power switch pulls
one of the ADB-cable lines down to ground. This sense line has a very
high source impedance, and it didn't take much current leakage to
ground to false-trigger it.
The Mac II was in a spare bedroom that got quite cold at night during
the winter (the place we were renting had a lousy heating system and
no insulation). In the morning, my wife would take a shower, humid
air would flood the back of the house, some moisture would condense
inside the cold keyboard case, and a few microamps of current would
leak across the switch contacts. BONG!
I cleaned the keyboard's PC board in the area of the switch with some
alcohol, coated it with something insulating (I think I used a thin
film of my wife's acrylic nail polish) and the problem went away.
So, I'd suggest inspecting the power switch and the PC board around
it. Possibly some old flux, or the dreaded "yellow glue" on the board
has become conductive with age. Clean it all up thoroughly (careful
scraping, flux-remover spray, etc.), dry well, and apply a conformal
insulation coating of some sort, and see if that resolves the problem.
Looking at the manual for the RD-6106 (which may be similar) - this
receiver does seem to have a "soft" power switching system, where the
main AC voltage can be controlled by both a "hard" switch, and by a
relay system driven from the control logic. The control logic then
looks at a "standby" pushbutton... this is a low-level contact closure
and seems to be tied in with the main keyboard scanning logic. So, a
contaminated "standby" PC board / assembly might be at fault.