Hi Eric,
EDIT:
I checked your motherboard model, and as far as I can see it has an RS790GX which is a RS780 integrated in the northbridge on bord and thus it has no fan whatsoever.
In this case a GPU fancontroller would, ofcourse, be impossible without fan.
However: If you also have a discrete and actively cooled RS780 GPU card, and disabled the on-board GPU, you might read on.
This might be a bit difficult: My script, as is, only works on "AMDGPU"
The RS780 is quite old and is not supported by the "AMDGPU" driver but by the "Radeon" driver which is quite a different beast.
I am a bit familiar with the old ATI "RS780". I used to have a laptop and a motherboard with a RS780 onboard (long long ago) and assisted a little bit in the creation of a kernelpatch for the, in some cases, somewhat unstable PLL behaviour of that chip.
This is a chipset of the "R600" family,
Details can be found here
If you have installed lm-sensors it should list the fan if the parameters are available. ( see also this post )
If the fan is not listed, the driver does not offer the possibility to influence the fanspeed. Also, if there is no sensor listed you can not get the temperature.
To list what your system offers with respect to these parameters you can use this command:
find /sys/class/hwmon/*/fan* |while read line
do
echo -ne "$line\t"
cat "${line%/*}/name"
done 2>/dev/null
It will list all fans detected with the name of the chip/driver it is connected to.
On my system, the relevant part of the output gives me this:
/sys/class/hwmon/hwmon1/fan1_enable amdgpu
/sys/class/hwmon/hwmon1/fan1_input amdgpu
/sys/class/hwmon/hwmon1/fan1_max amdgpu
/sys/class/hwmon/hwmon1/fan1_min amdgpu
/sys/class/hwmon/hwmon1/fan1_target amdgpu
If your chip/driver is not listed, then there is no way to get it working with my script.
However, if it is listed, there is a possibility that the script might be adapted to the parameters c.q. driver/kernel variables that /sys/ has offer. Beware though that this is highly experimental territory. 