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I hate to ask this, but you are turning them ALL the way off right? When mine are turned on to intermittent, they "park" halfway up then cycle up and down, then back to halfway up until I turn them off.
It could be just coincidental that your motor is starting to go, or you got some moisture in it, right at the same time you installed the new light stalk. A new "re-built" wiper motor from Autozone is about 40 bucks, and takes about an hour to install.
Since they aren't controlled by the same lever, it can't be that. Run us through the whole scheme....I turn wipers on they do this, I turn them off they do that. Maybe that will help someone narrow down your problem.
There is a connector on the lower left side of the steering column. It has 5 wires, pink, gry, dk grn, ppl, yel. ( the connector has 6 cavities- one is empty). After you find it turn the ignition switch to on, turn wiper switch to off, disconnect the connector. If the wipers park there is a problem with the wiper switch. If they did not park it is either a short in the power supply the yel wire or the wiper motor.