I actually checked the X-axis in two ways, but filmed only one. The biggest challenge with the baby-bridgeports which have long tables and relatively narrow saddles is "end sag or droop" when the table is cranked out in a cantilevered manner. That was the primary issue I was trying to correct, in fitting and adjusting the gib in the X-direction and why I concentrated on that in my video. When adjusting a gib, it's usually assumed that the gib is properly fitted to the dovetail and making consistent contact along the dovetail surfaces when dialing-in the gib screw for proper table tracking and movement. Having helped a few others with their benchtop mill gib adjustments, I have come to know that the gibs are often poorly fitted in the first place.
My PM935 exhibited far more table sag up/down than it did lateral table twist. I was having a terrible time trying to attain vertical tolerances on long part machining (20"). Even when the gib was fully wedged and the locking levers cranked down hard, I was getting teeter-totter movements that I felt were excessive. In my tests, the X-axis gib was found to be contributing to that issue far more than the Y-axis gib. By bluing up the gibs and looking at the interface in the dovetails, I was able to determine the X-axis gib taper and flatness was many thousandths off from one end to the other, and the gib was also slightly twisted. It was obviously never properly fitted to the dovetail in a precise manner. I was able to get that sorted by first properly fitting the X-axis gib (filing and stoning and checking flatness) then turning to the Y-axis gib (which turned out to be a minor contributor). I spent most of a day doing all this, an in my moment of joy getting this sorted, neglected to film and discuss the X-axis vertical check.
But assuming the gibs have been properly fitted, the recommended check in the X-axis is to indicate from the saddle to the side of the XY table and apply lateral force as you suggest. Same is true for the Y-axis check. I ended up doing both vertical and horizontal checks, but the gib
fitting culprit on my mill was the most vexing, and pulling up/down on the XY table was the best evidence check. Once I got that aspect resolved, the lateral movement check showed no further issues.
Here is a link to one of the very few gib adjustment checks I have seen documented that attempts to make the process empirically based, rather than just based on "feel." Check out page 6 in that document, and the diagrams on page 5 that illustrate the indicator setups. Most typically, the gib adjustment process is as described in the PM-935 manual:
"Aim for the best compromise between firmness and reasonably free table movement. Too tight means accelerated wear on the ways, leadscrews and feed motors, if installed. Too free means workpiece instability, inaccuracies and chatter."
I prefer the Wells-Index method.
Here is another video on the topic of ADJUSTING gibs using the Wells-Index method - again, assuming the gibs are fitted properly to begin with.
As for fitting a gib, in my case, the gib needed a lot of work - far more than I have seen needed on another other machine I've worked on. Most of the fitting was done with smooth files, and the stoning work was mostly for final flattening and burr removal. Keith Rucker goes through the process of making and fitting a new gib
in this series, episodes 19-21. I don't have access to a surface grinder, so I did as best I could with files and stones. It's not perfect but it's a lot better than what I started with and sufficient for my needs.
As for stones, most of mine are Norton benchstones, with two grits. I have three identical stones, one is a beater, the other two I work hard to keep flat. I also have a pair of precision ground stones that are the same Norton units ground to tight tolerance, which is what I use to stone the table top, vise base, etc to remove any dings or irregularities. The precision ground versions are available from Lance Baltzley
here. That rectangular stone on the far right is what I have. More on the precision stones is
here.
Hope this helps.