B-rad… have you removed the gear on your 292 distributor so you can install the one for a Lincoln? If it is off, buy a new FE gear and forget all this. As Ted said place the new gear on the 292 distributor shaft and get it close as you can..try both ways. 
 The gear does not need to be indexed. There is enough adjustment to get the timing correct as long as you have the rotor of  #1 aiming at the #1 spark plug wire you’ve placed in the cap and you 30* of movement for the vacuum can. 

56 Vic, B'Ville 200 MPH Club Member, So Cal.

When you install the new distributor gear, a couple of things must happen in order to use the existing hole in both the gear and the shaft.  This is assuming that the hole size in the gear is correct for the shaft being used.  Aftermarket and some special application distributors tend to use varying shaft sizes which in turn requires gears with matching hole I.D.’s.

1. The collapsed measurement of the distributor gear on the replacement distributor must match the original measurement.

2. The hole must be perfectly aligned.  Try turning the gear 180° if the holes fail to align.

In the event there is a problem with either #1 or #2, then the gear will need to be repositioned ~90° and a new hole drilled in the shaft using the existing hole in the new gear as a guide. 

Keep in mind that it’s rare for the holes in the distributor gears to match up with each other.  And those holes in the distributor gears are often slightly off-center which complicates drilling the hole in the shaft.  If you find that the hole in the distributor gear and the shaft do not match up, try turning the gear 180° on the shaft and see if that helps.  If no match, then a new hole in the gear and/or shaft is required.

Lorena, Texas (South of Waco)

Don’t beat yourself up too much. I’ve done worse on things like that, and I’ve got a drill press.

miker
55 bird, 32 cabrio F code
Kent, WA
Tucson, AZ

You won't if you got a good replacement gear.

Y's guys rule!
Looking for McCullouch VS57 brackets and parts. Also looking for 28 Chrysler series 72 parts. And early Hemi parts.

MoonShadow, 292 w/McCulloch, 28 Chrysler Roadster, 354 Hemi)
Manchester, New Hampshire

Why will I have to drill a new hole in the distributor shaft if the gear holes and existing holes line up?

Brad
Sierra Vista Arizona
1954 Lincoln Capri

Drilling a new hole in the original gear 90* from the original hole would work but Brad mentioned a new gear is on the way.  The goal now is to get the new gear pressed on the "new" distributor shaft in the CORRECT location and drill with precision a new hole so as not to ruin the new distributor and gear. Good luck.................

64F100 57FAIRLANE500

Drill a new hole 90 degrees from the old ?  I have seen it done


54 Victoria 312;  48 Ford Conv 302, 56 Bird 312
Forever Ford
Midland Park, NJ

Here's a pic of the hole I made


Brad
Sierra Vista Arizona
1954 Lincoln Capri

Do a Google search for the part number and follow the link to check. https://nospartsltd.com/product/fab12390c/

Y's guys rule!
Looking for McCullouch VS57 brackets and parts. Also looking for 28 Chrysler series 72 parts. And early Hemi parts.

MoonShadow, 292 w/McCulloch, 28 Chrysler Roadster, 354 Hemi)
Manchester, New Hampshire

The distributor I'm putting it on is fine, no issues getting that pin out. The one I took it out of, the Lincoln one, is cracked but all I needed was the gear

Brad
Sierra Vista Arizona
1954 Lincoln Capri