Question

What is it about our body that causes us to 'stick' to the source in case of an electric shock?

Answer 1

The electrical impulse will trigger the muscles to contract, making your hand impossible to remove from the source.

Explanation:

If you grab something with your hand, your muscles will contract and you grab the object even tighter.

I have always imagined myself it as following:
You place your hand on the source of the electric shock, for example on this part of the engine.

Then your hand will contract, which results in making better contact with the source and you cannot open your hand anymore. This results in your hand 'sticking' to the object. It is like having a cramp in your leg.