If it's an '88 and has the pushbutton unit, it'll be the same as the 126 and 124. They don't catch fire like the earlier units do, they're solid state from the 1986 year model instead of mechanical in a 2-part job like the '80-'85 cars were. You likely have a failed blower control module, it's a transistor pack with a heatsink on it. No idea where it is on a 201, on the 126 it's in the blower housing so it gets airflow. If your brushes were bad, it likely caused it to fail shorted, so it'll run the fan any time the key is on, regardless of what the pushbutton unit tells it to do.

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Current stable:
1995 E320 149K (Nancy)
1983 500SL 120K (SLoL)

Black Sheep:
1985 524TD 167K (TotalDumpster™)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)