The isur of amira lleakum came out in order not to weaken by being all the work of shabbos through a goy thereby eliminating shabbos altogether. Such that if he has no goy he might do it himself. Rambam hilchos shabos (6,1, ) so we can say that this can apply on a shabbos clock also. But if there is a mitzva, he will realize that their is a limitation on the permission. As I mentioned before that oneg shabbos might be considered a mitzva.
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