Hi,
safety first: be careful. you are working on dangerous mains voltage!
Disconnect the whole machine from mains before you touch, connect or disconnect a wire.
*****
what am I doing wrong when checking the SSR?
I assume the brake needs power to release the spindle and it may turn. If the power to the brake is disconnected then it brakes and the spindle stops running.
Therefore you need to connect the wires at #1 and #2 to release the brake. Can you confirm this?
There may be many informations around with a description how a SSR works. Read them carefully.
* #3 and #4 are the connections to an LED (inside the SSR, you can´t see it). An LED needs current, DC current .. and the voltage is of minor interest. Therefore to simply test the voltage is about meaningless.
(In detail it depends on the internal circuit of the SSR)
* you could connect a current meter is series with the line on #3 (or #4), select DC current. and tell us the measured values.
if I hook up #3 and #4 and turn on the machine I have 110V at #3.
This tells me you measure the (AC?) voltage against earth ground or something else.
If you want to measure the voltage then connect one wire of the meter to #3 the other wire to #4 and select "DC voltage". You could tell us the result of the measurement.
***
Connections to the brake:
When the LED is ON, then typically the relay connects the terminals #1 with #2. This switch is controlled by the light of the LED.
Klaus