I am assuming that the heating element has the two legs of the 240 v connected to it and that I should see 240 volts across the two connectors when running?
That is correct.
I do not and actually it reads just a couple volts. When I take one of the wires off the element and test I will see 120 v. Why is that?
I am not sure what you are doing when you measure the 120 volts.
Is one meter lead on an element connector and the other on the frame/Neutral/ground?
Also was the motor running when you did this?
Using the wiring diagram.
If the motor is running and you are checking from a heater connector to ground you would see 120 volts on the left hand side (BK). The circuit path is L2 , motor's centrifugal switch BU/BK (closed when motor is running) , heater connector.
Now here is where it gets a bit tricky. If the element is good but the other side of the element has an open in the circuit , then you see 120 volts on both sides but it is the L2 voltage on both sides. Neutral is not normally part of the heater circuit so no voltage is dropped across the heater so you see the same volts on both sides.
If the circuit path on the other side of the heating element is good then you will also see 120 volts but it is the L1 voltage so there is 240 across the element and it heats up..
Just in case you do not know how 240 works.
Your power is actually two 120 volt power supplies when referenced to Neutral but they are 180 degrees out of phase. So when one is at positive 120 the other is at negative 120, that is how you get 240 volts. The heater runs between these two supplies (L1 and L2). Neutral is not part of this circuit.
Now for the right hand side of the heater circuit.
BR on the heater , HI-LIMIT thermostat , PU and the contacts of the CYCLING thermostat , red on the TEMP SWITCH , the RD (red) to BU (blue) contacts are closed in any heat mode , BU at TIMER contacts 3 also closed in any heat mode , to the contacts a TIMER contacts 4 also closed, BK (black) to L1.
Now for some testing
With the unit unplugged and the timer set to mid scale of a heating mode.
You should have 0 ohms at all points from L1 to BR on the heater circuit. Use the most sensitive meter scale.
Can also do this with the unit (motor) off but connected to power, then you should see 120 volts at all points.
Using resistance is just a lot safer.
I hope I did a decent job explaining and have not confused you.