Well, mistakes need to be pointed out, glad you did.
There isn't any kind of feedback to the pilot indicator, it's a separate parallel circuit inside the flasher, flashes opposite the signaling bulbs. Flasher is activated with positive voltage at L terminal, so there shouldn't be any current flow through the flasher in center position Most suspect is the flasher itself, something conductive between X and P terms. Try cleaning base and socket with alcohol swab.
Of course, this assumes a standard 3-pin thermal flasher.
One other thought - if you wired tail lights as turn signals, you could have a pinched wire inside the t.s. switch. Tails are on with any other lights, so the tail switch wire is hot.