Vintage rain lamps will either need restringing, a new motor or both. If restringing the lamp does not solve the issue, then a new motor will need to be added; however, finding the necessary parts or a whole new motor altogether can be a challenge.
To restring the fishing lines, remove the old ones with scissors. Clean the thread holes to remove any oil build-up by threading a needle through the holes. Tie a knot at the end of the fishing wire large enough to secure it, then thread it through the first hole and pull it to the base. Continue the pattern until the lamp is restrung and tie a knot at the end to keep the wire secure and taut. Replace the foliage, statue, and light bulb then screw on the top canopy and bottom cage. With the lamp turned on, slowly add mineral oil until the raining effect looks normal. Do not add more than three pints of oil as it will overwhelm the motor.