The wiring diagram would have been a sheet of paper so it sounds like it was not there. Sometimes they are on the back of the dryer.

Here is a good link that may be useful.
http://www.applianceaid.com/ge-dryers.html

Check out Item 28 Sample Wiring Diagrams, there are a couple GE's.

I would check the heating elements.
Remove all wires from the elements. Then check them for resistance looks like they should be around 20 ohms.
Them check each element connector to the case. all should be infinite ohms.
If not the element is rounded and depending how it is grounded, it can keep the element on all the time so it never shuts off so the timer never advances in auto modes.

Be sure to note where the element wires go. You would be surprised how many folks forget where the wires actually went.

Here are your parts
Replacement parts for General Electric NJSR453EW2WW Electric dryer | AppliancePartsPros.com

This unit is made by GE so getting tech info is difficult, they like to keep all info a secret.
Do you have the wiring diagram?

Is the timer advancing or is it advancing to Off but not shutting off?
Does it do this in both timed dry and auto modes?

In timed dry, the timer motor gets power through a timer contact directly from one side of the line (120 volts).
In auto, the timer gets power through one of the heating element when it is shut off. The resistor (Item 80 in Section 1) then reduces the240 volts heater voltage to 120 volts for the timer motor.