This command makes an armour stand face the executioner's eyes, even though it should face the feet:

/tp @e[type=armor_stand] ~ ~ ~1 facing entity @s

The coordinates here are arbitrary, it works the same with ~ and ^ and even when not changing the armour stand's position at all.

This command makes an armour stand face some point above the executioner's head, probably as much higher than the eyes as the eyes are higher than the feet:

/tp @e[type=armor_stand] ~ ~ ~1 facing entity @s eyes

This does not happen if the execution context is anchored on the executioner's eyes. This command properly faces the feet:

/execute anchored eyes run tp @e[type=armor_stand] ~ ~ ~-1 facing entity @s

And this command properly faces the eyes:

/execute anchored eyes run tp @e[type=armor_stand] ~ ~ ~-1 facing entity @s eyes