Fuse? For what? The modes are not electric.
Although I agree with the best way to check the system is the vacuum pump method Hutch used in his video, to go with Hutch's GREAT VIDEOS on troubleshooting junk, the first few minutes of this one has him using a handheld vacuum pump to test each diaphragm.
If you can change any air flow anywhere, but not get them out the vents, then the purple tube has vacuum. You haven't told us where the air is coming out of when in A/C mode.
The temperature lever controls a cable to the blend door to adjust for hot or cool air (or both if in the middle somewhere). If in cold, it will use the 2 port vacuum valve on the HVAC control unit to shut off the water valve on the back of the intake.
Your mode selector valve (9 port valve on the HVAC control) may be leaking so bad that you won't get any diaphragms to to move. Do you hear a hissing noise from the HVAC control unit when the mode selector is in various positions? That's a rare bird to find if it's the 9 port valve leaking and costs accordingly to find new. You may have better luck trying to fix yours. Usually the plastic center pin wears/loosens up causing leaks.
Assuming you're getting air flow SOMEWHERE, most likely the floor, it may be your lower mode flapper stuck in the up position and possibly the dual action diaphragm isn't working or strong enough to move the flapper. Or the upper mode diaphragm may be hosed, and the defrost door defaults to the defrost mode when there's a lack of vacuum there.
Note: The service manual seems to be wrong on the part where it says when the upper diaphragm for the defrost valve is vented the valve is "closed." The defrost valve defaults to the defrost position when vented. So the GM engineer who approved that figure wasn't paying attention to details. It's confusing for sure, though.