The contacts are large, but in normal use will contact at one specific point only. With use, that spot will burn/corrode/etc., but if you turn the switch at a different angle you will be using a "fresh" surface. The corroded surface has resistance, the "fresh" surface does not. This resistance is too small to measure with a multimeter (unless you can do a 4 wire measurement at $1000+ for the instrument), but is enough to prevent the starter solenoid from kicking in properly. You might me able to clear the problem with contact cleaner spay (don't use the cheapest one, it "melts" some plastics) and/or fine sanding paper. The problem occurs when you/previous owner does not fully turn the switch to the start position, resutling in a small contact surface which heats up and/or arc. Can also occur due to a (previously?) faulty starter motor solenoid. Have fun...