THere is a reference in the Greenberg book to these cases, which Gilbert did acquire as war surplus and used in the early 1920s to house both tool chests and the 1924 No. 10 Erector. Whether the lock you mention was a Gilbert addition or not is an open question.
As to tool contents, I am not aware of any well developed inventories for the various sets. It is not unusual to find these sets with only a few of the tools, and with tools not in the sets mixed in. After all, they were tools and over the years were used as such and mixed in with other household tools, etc. I have an early 1920s tool chest which does contain a decent number of tools that appear original, but I do not recall that any were marked as Gilbert.

Putting a new power cord on an Erector motor is straightforward. The leads on the cords are soldere to the leads inside and then wrapped with electrical tape. Getting off the old friction tape will usually require some work with an exacto knife or equivalent as it is often pretty dry and brittle with age. The main challenge is that there is not a lot a lot of wiggle room in any of the motor cases. So placement on reassembly has to done carefully. One other thing is that in removing the rotor, be careful not to lose the small insulating washer spacers on the axle.

THe electromagnets are not as difficult as you surmise. The earlier large magnet cases are held on with a screw and small double angle. remove the screw and the actual magnet assembly is removed by pulling the rotted wired through the hole in the case. The smaller red magnets have a round hook at center outside the case, but it is actually a screw end. Unscrew it and the case and magnet pole come apart the same way. the two wire leads are soldered to the ends of the lacquered wire on the windings. Remove the old leads and replace them with similar gauge mew wire leads which will pass through the 2 holes at the top of the magnet insulator, resolder to the winding wire. But if there is a break anywhere in the winding, you would have to rewind the magnet. In that case you could the number of turns in removing the winding and then rewind with the same number. And if you are off a bit with the magnet, it is not as critical as it would be rewinding a motor pole.

I’ve seen that screwdriver on ebay. Doesn’t look right to me. I suspect that it may have been found with a mixed part lot that included a coal loader cover manual with a 1938 copyright date. There are more “1938” sets listed on ebay by seller who assume that the copyright date on those coal loader manual covers is the date of manufacture of the set. The wood handle screwdrivers in pre-war sets have handles that are similar to the handles on tools in the Gilbert Tool Chest Sets. The post war wood handle screwdrivers have a different, sort of bulbous wood handle. But neither looks like the one on that ebay listing. The screwdriver is familiar as I have one kicking around somewhere that has been around since I was a kid. I believe it was either from a Buildo construction set or a kid’s tool set that was not Gilbert.

Red and Green screw base bulbs are generally available through dealers in replacement Lionel and Flyer train parts. I would assume 18 volt bulbs would be right. Try the Train Tender website.

Restore or not? Always an interesting discussion. But it really comes down to what is it that you are trying to achieve. I recently purchased an incomplete set with a ton of potential. But it is one that is unlikely to ever reach a point where all parts are pristine originals. Some of the painted parts were in need of help, while the hunt for some of the original parts for the set is one where these are so scarce that it will take years and still will likely come up short. So I will repaint, even though as many know, finding the shades can be a hunt in itself (I have yet to come across a perfect match for the red-orange/orange-red for those 1920’s era sets, even with mixing my own paints.) And I’ll make the missing replica parts that are difficult to locate. And this is because I want the set to simply have what it is supposed to have, and ultimately use it to build the feature model when reaches that point. Original is fine if it is good original. A set that might be all original but looks like it went through the wars? Not going to be of much value really except as something to be broken up and sold piecemeal. But I’m not really into value as almost all my stuff traces back to flea market days before ebay changed the landscape. So I want them to look good and be useable, but I always bear in mind that in the end they are still toys. And, after all, Type II reached it’s end in 1963, and Type III in 1987- or approximately 60 and 30 years ago respectively. That means that the number of people who know of and are interested in these sets is on an ever downward trend. So value, as with all collectibles, may be something of an illusion. The last man standing just may be able to have the greatest Erector collection of all times if he keeps a sharp eye out what what is sitting along the curb when that day comes. As such, I see the real answer can be found in a 5 word reply – Do what makes you happy!