Happy new year to all!
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The Leslie control schematics show a SPDT contact set relay with a pair of 0.1 ?F capacitors (C621, C622) across the points. No resistor. Yes, due to their age these capacitors are the first suspects and can/should be replaced without measurements. But also check the suppressor diode (D607) across the relay coil. It must not be open (OL) with your DMM's red probe at the anode and the black one at the cathode. This inhouse numbered diode can easily replaced by 1N4007 or the like.
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Best regards!
Uwe Menrath