On my Hot Shot, only 1 special lamp lights at a time. It alternates between the left & right standup targets, controlled by a make/break switch on the A relay. It sounds like you might have an inadvertent make/make switch on the A relay instead?
If a special lamp is lighting, then the AX relay has definitely pulled in.
Do the standup targets score points?
In order to score a special replay, the circuit shown between rows 6 and 7 on the schematic should come into play. There is a long series circuit.
Thus, a motor switch (green-black wire) at position 1C needs to be conducting, along with closure of the (lit for special) standup target switch, along with one of the make/break switches (yellow wire) on the A relay (there are 5 m/b switches on the A relay), along with a NO switch (yellow & red wire) on the AX relay, along with the 15th position switch on the credit unit itself. The game will not score a special if you already have 15 games on the credit unit.
Let us know if all those switches check out.
Lee