That was an enthusiast device. When new, it didn't come with a remote. And it didn't have Sony's S-Link connector in the back either (popular at the time with other Sony devices to link together for control).

Your best option for still finding a power control solution, will rely on the old 'System Power Commands' that Sony used during the 90's. It was a generic OFF & ON command that all Sony devices would respond to. So sending the 1 System Power OFF command would cause multiple device to shut off (TV, Amp, VCR, etc.). And similar for the System Power ON command.
It might respond to those power commands.

In the URC database, go under AVR's and Amplifiers. Go to Sony, scroll to the bottom with just the #codes for database entries [Sony 1 thru 107]. Go thru all 107, testing each one (I would make a test file on the MX980, with 107 devices and go thru them all in 1 shot).
If the 707ES doesn't respond to any of those power commands (or tuning commands for the ones that have it), then the device simply does not respond to any IR codes for those features.

You can use a remote AC outlet, to shut power off to the 707ES. Although it probably doesn't turn back on when power is restored, so still has to be turned back on manually.