There are a few systems:
(1) Ones like MINE, a 1978 C15 without air and without a relay, rely on the switch to do all the heavy lifting.
(2) Ones like mine, without air, but that use a relay, so the switch doesn't do any heavy lifting (it just activates the relay/relays).
(3) Ones with air, and that use a relay to feed the blower. In those, the switch activates they relay, rather than feeding the blower directly.
(4) NOTES and RAMBLING:
4.1 If a single relay is used, the relay has to have an input and output terminal for each speed.
4.2 The alternative to a single relay for all speeds would be, a relay for each speed. One advantage would be, even if one relay went out, the others would work, so you could, for example, have low and medium fan speed, and no high speed, or low and high, but no medium. . . .
4.3 For the relay inputs from the switch and outputs to the fan/blower resistor, you'd have a wire for each speed from the control switch.
4.4.1 ALL of these systems had a constant on blower.
4.4.2 MY switch, for my three speed, non-relay system, had gone south. I replaced it with the four speed version. By not wiring the first speed, I, now, have an off position.
4.5 The heater blower is on only when the ignition is in the run position, No power goes to the heater control unit when the ignition is off, or the accessory positions (unless it's been tampered with).
4.6 For MY rig, the heater blower fuse is at the top right of MY fuse box, and is, clearly, labeled.
4.7 MY heater blower uses 14 gauge wire.
4.8.1 For MY C-15, a brown wire runs from the heater fuse to the top terminal of the heater control switch connector. From there, a second brown wire goes straight to the low speed connection on the blower resistor, to create the constant on [low] effect.
4.8.2 Blower high speed is via the full 12 volts, all the other, lower speeds, are via the dropping resistor on the firewall.
4.9 The factory control assembly switch connector works with both 3 and 4 position switches.
4.11 If the resistor is bad, and because high speed bypasses the resistor and goes straight into the blower motor, you should still have high speed, even when lower speeds are dead.
4.12 Because the system relies on tapping the coil resistor at different places for different speeds, the resistor COULD break (open) at one end and still work for one speed.
4.13 If the connection or wire out of the resistor to the blower is bad, none of the speeds should work.
4.14.1 To convert MY system to one with an off position (four positions), I had to shuffle wires around on the switch connector. See examples of before and after, below.
4.14.2 Altering the switch wiring configuration included separating the two brown wires so the fan would have an off, low, medium and high. See attached photos of MY switch connector.
4.15 I'm thinking of adding the three relay approach to mine just because I can, and because I'd still have defrost and heat when one or two went out.
4.16 Generally, relays are cheap, and dependable.
4.17 With power off, you can use an ohm meter to determine the input and output terminals of your control switch.
4.18 If the relay easier to get at, versus pulling the switch, and with the ignition switch in the on position, you should be able to read 12 volts into the relay with the switch on high, medium or low (the wires out of the relay to the blower (high) or resistor (medium and low).
4.19 If you pull the switch assembly, with the connector plugged in, you should get 12 volts on the input from the fuse, regardless of which position the switch is in.
4.20 You can move the positive test lead to other terminals to read the voltage out of them and that feed to the relay or resistor switching through the switch positions. For example, switching to medium, then moving from the input to other terminals, one of them should give you 12 volts again. Then the next speed should give 12 volts at another connector. . . .
4.21 Interesting that ones like mine don't use a relay [and it isn't shown on schematics or wire diagrams], because the same amount of power passes through the switch to the heater in all speeds. It's just that, to get the slower speed, some of the power through the switch is, farther down the line, dropped across the resistor.
Hope that gives some helpful info.