Straight rubber connector pipe.
The standard vacuum advance distributor is connected to the carb / manifold by a small rubber joint that in turn is mated to metal line that fits the distributor.
If the little rubber connector is deteriorated, it could allow a vacuum leak at the carb and stop the advance from working properly.
When in doubt replace it.
Recommend: 1 x 12B2095 per Mini.
For the angled rubber connector, see 12B2062
For the vacuum pipe with both connectors, see 37H4229M