1998 Ford E-350 Rear Heat Issue....

It sounds like it is a vacuum problem but you should check all other vacuum accessories to make sure if they are operating normally or if they have a degraded performance. If others are ok and obviously rear heater control is not then I would investigate the vacuum hoses or the control itself and not the pump. If you have access to a vacuum hand pump put it on those levers you said you pushed and see if they actuate as that valve itself could be faulty. As far as the brakes go decreased vacuum should not cause them to drag, it would cause increased peddle pressure required for application but shouldn't have an adverse effect on release, things that may cause brake drag at the rear are, rear adjustment, maybe defective or swollen brake hoses impairing return of the fluid, blocked port(s) in the master cylinder, extremely worn backing plate preventing shoe to return properly, damaged or missing return springs, and even possibly a siezed parking brake cable. You are going to need to remove the rear drums and inspect the brakes to make sure that everything looks as it should, use a prybar or screwdriver to gently pry up on the shoes to see where they ride on the backing plate and make sure there aren't large grooves worn in, I have smoothed these down in the past but depending on wear the backing plate might need to be replaced. Also make sure that the springs are both there and actually remove them to make sure they retract into nice tight coils, if they are stretched then the shoes won't return properly. The wheel cylinders should not have any fluid leaking at all, there should be a protective rubber boot on both sides of the wheel cylinder to keep out dirt and brake dust, these are not for fluid sealing, use a small flat blade screwdriver to gently pull the boot up partially to look, if you see an abundance of fluid that is a problem if it looks like it is "sweating" that is a sign that they should soon be replaced but "shouldn't" be causing the dragging problem. With the brakes exposed make sure that the parking brake cable is releasing completely, and not pulling the brakes into a partially engaged state, even if this is engaging a small bit but not causing continuous brake drag, it may be causing disengagement problems. When reassembleing I usually reinstall the tire (easier to turn axle) and tighten the brakes until I hear the shoes starting to come into contact with the drum, then step on and release the brake peddle (putting the shoes into normal released position) and adjust again, this is the optimal postition for the brakes to be adjusted to. After that has all checked out and with the brakes readjusted I do a couple of quick tests to make sure the brakes are working and go for a small road test to see if the problem has been rectified. If not I would assume the master cylinder as the chances of the hoses themselves swelling is unlikely if you have not added fluid or you have used the reccomended brake fluid. It sounds like it is a vacuum problem but you should check all other vacuum accessories to make sure if they are operating normally or if they have a degraded performance. If others are ok and obviously rear heater control is not then I would investigate the vacuum hoses or the control itself and not the pump. If you have access to a vacuum hand pump put it on those levers you said you pushed and see if they actuate as that valve itself could be faulty. As far as the brakes go decreased vacuum should not cause them to drag, it would cause increased peddle pressure required for application but shouldn't have an adverse effect on release, things that may cause brake drag at the rear are, rear adjustment, maybe defective or swollen brake hoses impairing return of the fluid, blocked port(s) in the master cylinder, extremely worn backing plate preventing shoe to return properly, damaged or missing return springs, and even possibly a siezed parking brake cable. You are going to need to remove the rear drums and inspect the brakes to make sure that everything looks as it should, use a prybar or screwdriver to gently pry up on the shoes to see where they ride on the backing plate and make sure there aren't large grooves worn in, I have smoothed these down in the past but depending on wear the backing plate might need to be replaced. Also make sure that the springs are both there and actually remove them to make sure they retract into nice tight coils, if they are stretched then the shoes won't return properly. The wheel cylinders should not have any fluid leaking at all, there should be a protective rubber boot on both sides of the wheel cylinder to keep out dirt and brake dust, these are not for fluid sealing, use a small flat blade screwdriver to gently pull the boot up partially to look, if you see an abundance of fluid that is a problem if it looks like it is "sweating" that is a sign that they should soon be replaced but "shouldn't" be causing the dragging problem. With the brakes exposed make sure that the parking brake cable is releasing completely, and not pulling the brakes into a partially engaged state, even if this is engaging a small bit but not causing continuous brake drag, it may be causing disengagement problems. When reassembleing I usually reinstall the tire (easier to turn axle) and tighten the brakes until I hear the shoes starting to come into contact with the drum, then step on and release the brake peddle (putting the shoes into normal released position) and adjust again, this is the optimal postition for the brakes to be adjusted to. After that has all checked out and with the brakes readjusted I do a couple of quick tests to make sure the brakes are working and go for a small road test to see if the problem has been rectified. If not I would assume the master cylinder as the chances of the hoses themselves swelling is unlikely if you have not added fluid or you have used the reccomended brake fluid.