Dial test indicators are similar to dial indicators, but are typically more precise and have a smaller range of movement. Rather than a plunger that moves in and out, they have a small lever arm with a ball-shaped tip that moves up and down. This enables the tip to be inserted into a small hole so that the hole can be precisely centered on the lathe axis - an operation that could not be done with a dial indicator. Check the typical import tool catatlogs (especially the sale flyers) and you should be able to find these from under $30.
The indicator shown here has a measuring range of 0.030 - much less than a dial indicator - and reads plus or minus from the zero point. When the tip is at rest at its neutral point, it can be moved 0.015 in either direction. The tip can be set at different angles for convenience in setup. As on the dial indicator, the bezel and numeric scale can be rotated to zero the reading. Each division is 0.0005 (5 ten-thousandths or half a thousandth per division).
On three sides of the DTI are small dovetails used to mount it. Mine came with two adaptors that attach to these dovetails and have short mounting posts of different diameters, as shown in the next photograph. The magnetic holder that my DTI came with also has a dovetail clamp which clamps directly onto the DTI body.
Here's a photo showing the DTI in use centering a bolt with a hole drilled in in in the 4-jaw chuck. You could not use a DI in this situation since there is no exposed surface of the bolt other than the hex head. Instead, we take the reading off the edge of the hole, taking advantage of the narrow ball tip of the DTI. Since the DTI has only a very limited range, you must have the bolt pretty nearly centered already before you can use the DTI. You can get pretty close by observing how far each jaw extends from the edge of the chuck and making these as nearly equal as possible.