That title should probably be "What to use to drill a mortise on a moulding plane" but the "how to" must start out with the right tool. The wide mortises are easy. There are several different options to choose from in a typical shop but what about those really narrow mortises. Like the number one to four sizes. Basically anything 3/16" and under.
I have done the gimlet bit thing. They are great if you can first of all find the narrow ones and they are not all beat up and crooked and dull. That is difficult to find and I never found a narrow one that cut correctly as is. If you do find them they have many times been attempted to be cleaned up to make look nice for sale on eBay and thus dulled even further or someone tried to sharpen them and might as well have ruined it. I wish they were easy to sharpen but it is about as hard to sharpen as is sharpening a spoon bit. Once they are messed with too much in the wrong way then it is a nightmare to get them back to right. Well, at least it is for me.
So now that I have scared you off from trying to drill your mortise with a gimlet (sorry) let me tell you what I use.
Ok so where to buy these little guys. I bought mine from a supplier in Germany. www.fine-tools.com. They are reasonably price but the shipping is costly, as you would expect. They sell a small bit brace that fits the hex shanked bits that I use. It is decent but I am going to make one eventually that is more suited to me. Of course you can use your standard two jaw brace and use an adapter or these bits can be used in a power drill, according to the manufacturer. I have not tried this myself.
I use the 3mm for the smallest wedges, the 4mm and 5mm for most everything else. If I had to suggest one it would be the 4mm since it tends to be one that I use the most.
Hope that helps you out in making those narrow mortises!