This is more likely. The base element usually gets damaged on the door side from being pulled and compressed when entering/exiting the vehicle. If you remove the seat material you'll probably see one or more black spot where it's broken the connection and sparked/shortened a few times.
Due to being wired in series, if either the back or base elements fails the whole system won't work. Both need to be functional for it to work. They're not cheap to replace (e.g. compared to the price of a complete electric blanket for a bed) but worth it in my opinion.
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