HGC,
I use a diamond core bit with a putty resevior around where I M drilling. Inevitably, the hole is slightly deeper on one side than another. As soon as I see that water come through where the core bit is drilling, I stop using the core bit and swith to the dremel.
I clip a small airhose tube on a large glass of water and tie a knot at the end so the gravity siphon only allows a drip or two per second. I put than in the putty area where the dremel will make contact and dremel with one hand and guide the drip with the other working the dremel bit up and down traveling no more in distance than the dremel bit has diamond coathing. I work my way around the already cut channel with the drmel until the hole falls into the towel I placed below to catch the excess water dripping.
Hope that helps, if I get another drill request, I'll video it and post accordingly.
HTH,
House