I've read about similar experiments in the past - covering the P patches with tape can sometime help clear it up. I've never tried it personally, but can see why it may work.
Covering the patch will reduce the amount of oxygen to the skin, causing the skin cells to become hypoxic (lacking in oxygen). Faster-growing cells need more oxygen, and so is likely to cause them to die in preference to normal cells. I would guess that less permeable tapes (especially the ones with vinyl or acetate backing) will be less permeable to air and hence better candidates for occlusion therapy. Please bear in mind that sticking tape over wounds and P patches may induce allergic reactions and further reddening of the skin, so take care. I wouldn't recommend it on large areas either, it may produce large-scale necrosis and oxygen-starvation to underlying tissues.
I've also heard, er, that covering ones body in tape is some people's idea of having, er, fun

This is certainly one way to include P in, er, fun

Coops