In this context, "перемикання ланцюга живлення стартера" is not necessarily a part of that illegal start-up procedure (by means of "буксирування" of the vehicle). Drivers in this part of the world, especially "дальнобійники" ("over the road" or "long-haul" drivers -- counterparts of "interstate drivers" in the US) or drivers working in agriculture farms as well as servicemen have traditionally been very inventive when it comes to illegal procedures :) They know a variety of other quasi-legal/illegal start-up procedures and even discover new ones from time to time. It is no surprise that they have no much problems using such methods routinely, especially when the air temperature drops to -25C (as it is the case today in some parts of Ukraine) or -30C. For instance, your starter can be connected to a battery of another vehicle, etc. So "перемикання" may refer to a different start-up procedure.

Therefore, it is better to translate it as "switching over / change-over / transfer" to be close to the source.