I have a patch kit (from Bike Hand) and it includes:
Along with the aforementioned supplies there are two small rubber tubes, hollow, and about 1cm long. What are these and how would one potentially use them with the patch kit?
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The little rubber tubes are for repairing Woods/Dunlop valves. The valve core does not have any valve mechanism in itself, but relies on the little rubber tube to seal. The tube fits over rounded end of the valve core shown below.
Most of new tubes come with similar-looking valve that has a ball and spring mechanism instead of the rubber tube.
The little tubes are for Dunlop valves. The tube is pulled over a stem. Air pressure will push the the tube against the stem and prevent the loss of air! https://en.wikipedia.org/wiki/Valve_stem If you look at the German translation of the page you find more pictures and one of the tubes in use. This type of valve was much used in England and also in Germany and has been supplanted by Presta and Schrader valves.