Ahhhh!! the secret weapon! I've read many stories and many laments over the years, about the difficulty of getting the tappings out of small holes, as they tend to clog the flutes and can cause tap breakage. I put a coupling on a small grease gun, tapped out to take the "needle" that comes with a air blow gun set, and I inject each hole full of grease before tapping. As you tap, the tap entering, pushes the grease and cuttings up the flutes and out, at the same time lubricating the tap.
Having just spent two and a half days tapping out some hundred and sixty or seventy #4-40 holes, I figured I needed a secret weapon, and it worked as planned, but I also learned considerable about small hole tapping. Of the six taps I broke so far, one was broken because I bottomed it out, four were broken because they were started less than straight, and one was broken by side force used in attempting to straighten out the start with too much force.
If you ream a good clean countersink after drilling, larger than the diameter of the tap, use a piece of steel with a guide hole drilled to start it straight, hold the tap holder between the thumb and forefinger, as close to the tap centered as possible. Pressing down on the tap, with feel, get all the flutes touching, by feel, start the tap, with slight pressure, but focus on keeping the flutes feeling even in their bite. Once you've got a full half turn that feels like the first thread has a full bite, continue to turn the tap while pulling up on the tap holder gently, this lets the tap absolutely follow the lead of the tap in the hole that exists, and allows it to ignore pressure in the wrong directions. Once you have two full threads started by pulling up, you will find that you just have to move your finger and thumb out a little at a time to gine the leverage necessary, to tap straiught in. If you do not hit a strong moment of opposition, tap straight through to the end. Otherwise, back off when it gets tough, enough to break the chips.
Mad Jack