The point of questioning the gauge of wire in this problem is moot because we are talking about such a short length of wire. Even if you incorrectly installed a higher or lower gauge wire, the wire resistance is negligible ... the wire size is not going to be a cause of the flipper feeling weak. Resistance of 10 ft. of 24AWG is about 2.5 ohms and resistance of 10 ft. of 18AWG is about .5 ohms. The main reason to go with an equivalent or larger diameter wire is primarily safety, as the circuits are fused for the current handling of the circuits and the fuse. Using the same wire size when replacing also tends to make splices and connectors easier to implement.

Measure resistance through your solder connections, not at them - to make sure your spliced connection points are electrically low in resistance. If the problem is not your splice then it is something else entirely (EOS, cab switch, mechanical issue etc...)

if the replacement switches do not have a capacitor, one should be added. A 1uf 500V disc capacitor is used across the flipper switch to reduce high voltage arcing and pitting. The cap will help lengthen the life of the switch.