My 2013 Macbook also had a display mux that switched the laptop display itself between the integrated and discrete GPU. In some cases it would fail to properly switch the display over causing it to remain permanently off until the next reboot. I was not the only Macbook user with the problem.
Apple is just as guilty for shipping laptops with hardware issues that you just have to work around. And unlike this Asus issue the Macbook mux was on by default. You had to turn it off in the settings if you wanted to entirely avoid the issue and then you would have no way of using the discrete GPU.
As did my 2015 Thinkpad - same problem, both an integrated and an external GPU, and I was constantly fighting with the drivers to get it to just make use of the external GPU. I'm plugged into a wall whenever the laptop isn't suspended/shut down for transport, stupid machine, stop making Autodesk and my games crash because you want to boost your battery lifetime numbers!
They had a special Lenovo driver that would occasionally become overriden by Windows updates but could be reinstalled manually, I dual-booted Debian though and getting the system to work properly under that was a nightmare. There were a couple years when I simply gave up, I got it to work with the iGPU and I wasn't running anything more graphics intensive than a browser so I simply left the discrete GPU idle while running Linux.
Incredibly frustrating.
I think all these manufacturers are desperate to get their published specs for battery life estimates to double-digit hours that can't be reached while running the discrete GPU at full speed all day. Heck, they can't be reached while running the CPU at full speed all day, you're not going to run a 35W processor and a 55W graphics card and a 20W display (10W when you arbitrarily reduce the max brightness when on battery power) all day.
You've got like 90 watt-hours available in the battery, at 100% usage on everything the real capacity is gone in under an hour...which is unacceptable. So Asus and Apple and Lenovo and everyone else have to come up with some hack to turn it off whenever it's on so that the spec sheet says you can get 8, 10, 12 hours of runtime.
We had dozens of 2013 MBP with discrete GPU mux where I worked. I bought one afterwards and used it until the M1 laptops came out, for pretty much everything you can use a laptop for. Never had or saw this problem in any of them, FWIW!
Was it a Fall 2013 or Spring 2013 Macbook?