Siegelzeichnerin

If the controller of the original spell chose to pay an alternative cost (such as prowl) or an additional cost, that choice is also copied.

If the spell is modal (that is, it says “choose one —” or “choose two —”), the choice of mode(s) can’t be changed.

Sigil Tracer’s ability can copy an instant or sorcery spell that isn’t targeted.

Since the activated ability doesn’t have a tap symbol in its cost, you can tap creatures (including Sigil Tracer itself) that haven’t been under your control since your most recent turn began to pay the cost.