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I won't make any assurances that replacement will resolve the noise, but the '87 wiper transmission (along with other years that used that design) are not well engineered for extended service. They loosen and become noisy. You maybe able to find an aftermarket kit to service the joints if you search patiently. Liberal lubrication of the joints with high quality, water tolerant lithium grease is crucial to long service life.
Remove the cowl (be careful so as not to chip any paint - it's safer with the hood removed). Grab the wiper arms and move them back and forth as you watch the linkage connections. Although the links may rotate a little on the ball joints, how much combined end-to-end play is there in the linkage between the wiper arm flags and the motor flag? A new OE transmission will exhibit virtually zero play. Excessive play is bound to generate noise as parts move relative to each other. If the transmission is quiet, it's probably not worn out.