The wiper relay is probably bad. It's a simple job to replace it, and I believe it's on the driver's side next to the main relay (somebody check your shop manual to confirm). If your intermittently intermittent wipers aren't quite what you want them to be but they do work at least some of the time, it's either the relay or the switch.

Since the wipers can at least come on once, we can assume the motor is fine but the signal going to them is bad. The signal is probably bad because of the relay (especially if they turn on once on intermittent but not again) or the switch (less likely, but if the wipers just don't notice that INT means ON, it's possible).

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