I suspected it might be the timer and so loosened the timer and then disconnected all wires from the timer with pliers and one by one reattached the wires to see which one would trip the breaker. I took lots of photos before I disconnected the wires so I knew how to reattach them. I also made sure every switch was set to off. Each time I attached a wire the breaker was off and then I would flip it on to test. Once I knew which wire I asked a question on an online help service - I paid $5 - and they told me I needed to replace the timer.
I bought a new timer and swapped it out and the dryer works again.
Changing the part was really easy - working out which part to change was the hard part. We spent hours studying the wiring diagram.