OK, guys, let me see if I've got this right. Some of this is guesswork, as I know nothing about the XLHs.
THROTTLE
1952-1969 all models - turning the right grip "in" (counter-clockwise as you're sitting on the bike) lengthens the cable, which opens the throttle. This pushes the K/KH carb rearward, and the XL carb to the right. The 56220-53 sleeve was used on the right handlebar.
ADVANCE/RETARD
1952-1956 K and KH - had a circuit breaker (timer). The advance/retard cable ran between the cylinders and exited in front of the circuit breaker. The timer advance/retard "peg" is near the front of the timer. Using the 56220-53 sleeve on the left handlebar, twisting the left grip "in" (clockwise as you're sitting on the bike) shortens the cable, turning the circuit breaker clockwise (looking down) - advancing the timing.
1957 XL, 1958-1964 XLH - had a circuit breaker (timer). The advance/retard cable ran between the motor and the front downtube, and clamped on the top generator bolt along with the horn - in front of the circuit breaker. The timer advance/retard "peg" is near the front of the timer. Using the 56220-53 sleeve on the left handlebar, twisting the left grip "in" (clockwise as you're sitting on the bike) shortens the cable, turning the circuit breaker clockwise (looking down) - advancing the timing.
1958 XLC/XLCH - the photo in The Legend Begins show the 1958 XLC/XLCH with the magneto's plug wires at the front. Later XLCHs have the magneto's plug wires at the rear. I'm not sure, but I think the 1958 magneto is fixed.
1959-1964 XLCH - used a fixed magneto - so there is no advance/retard.
1965-1969 XLH used an automatic advance circuit breaker, so there is no advance/retard.
1965-1969 XLCH - had an adjustable magneto. The advance/retard cable now runs along the left side of the engine, then turns and clamps under the oil tank - behind the magneto, and the magneto advance/retard "peg" is now at the rear of the magneto. Turning the left grip "in" would turn the magneto the wrong direction. So Harley used the 56220-58 sleeve on the left handlebar, and it has a spiral groove cut in the opposite direction as the -53 sleeve. Now everything works normally - as you accelerate, you turn both grips "in", opening the throttle and advancing the magneto.
Notes:
Why does the 56220-58 sleeve have a -58 part number? Perhaps the 1958 XLC/XLCH did have an adjustable mag. Or maybe they designed it for 1958, but never used it until 1965. Or maybe it was for the XLR. Who knows? Maybe DaveC?
Question:
What keeps the left grip from turning on the bikes with no advance/retard?