Julie-
Do you mean to tape a dressing around it or tape it shut? Most of ours are left open to air after the first post-op day. As for the mucous seeping, it could be months. Some peoples trachs are just really sloppy. I usually just put drain sponges around them under the trach ties and a wash cloth on their chest almost like a bib if it's really sloppy and I can't be in there every 30 minutes. If she's able to cough mucous through it it's better than anyone having to suction it. The tissue is probably still pretty irritated and that could cause the mucous production to increase. I would be really careful if you are taping it shut. She could form a mucous plug that could block her airway if it's not allowed to come out. Good luck!
BTW, I just noticed your siggy, you're almost done!