The adapter is installed in your gearbox. It is the part that the gearstick screws into. Here's a link to what it looks like.
 
https://www.ebay.ie/itm/ford-escort-mk2-RS2000-quickshift-gearstick-adapter-/362444227783?hash=item54635c04c7
 
In your photo of your gearbox & stick on page 1, I can see that the adapter is already installed in your gearbox. Without removing the adapter from the gearbox, measure the part of the adapter that is exposed above the gearbox extension housing which it screws into. The adapter should be 23mm high as that is the amount that the pivot point on the stick is raised as a result of the 23mm spacer between the nylon screw & the top of the fork in the stick (based on the measurements you supplied earlier). If the adapter in the gearbox is shorter than 23mm, then this would explain why you can select reverse without pushing the gearstick down. If the adapter was taller than 23mm, then you would have to push harder than normal in order to select reverse.
 
Here's a thought. Install the stick all the way in. If you're able to select reverse without pushing the stick down, then slowly start to unscrew the stick out, bit by bit, each time checking to see if at some point the reverse gate locks you out, and then let us know what happens.
 
Chuff

This is a standard gearbox:

 
This is the adapter:

 
This is the same standard gearbox with adapter installed (circled). It just screws into the gearbox. Take it out, and it's a standard gearbox once again.

 
The height of the exposed part of the adapter should be the same height as the 23mm section of your gearstick located below the threaded nylon section and above the top of the fork.
 
Based on your measurements, the pivot point of your RS stick is raised by 23mm when combined with the adapter, thus moving the pivot point up by 23mm resulting in a shorter throw at the top of the gearstick.
 
If the adapter is protruding out of the gearbox extension housing by 21mm instead of 23mm, then the notch in the stick will be too low and you will have no reverse lockout, which is, correct me if I'm wrong, what is happening in your case. On the other hand, if the adapter is protruding out of the gearbox extension housing by 25mm, then the stick will be too high and will require an extra 2mm of downward pushing in order to select reverse.
 
So, what is the height of the exposed part of the adapter which is installed in your gearbox and circled in the photo above.
 
Chuff
 

This is the photo you posted on page 1. Is this a photo you took of your actual gearbox?
 

 
 
Chuff
 

OK. That's a 2mm difference. Unusual.
 

1. Take the adapter off the gearbox.
2. Screw it completely onto the gearstick, all the way up to the metal tabs. I normally fold the tabs over at this point and insert the gearstick as an assembly.
3. Now screw this gearstick/adapter assembly all the way into the gearbox making sure the notch in the fork faces the driver's side.
4. Check to see if the reverse gate locks you out. It shouldn't, based on what you have already said & done in this thread.
5. Now unwind the whole gearstick/adapter assembly out of the gearbox by 2mm.
6. Check to see if the reverse gate locks you out. It just might.

 
Again, this is unusual. I've never known what the height difference is, 23mm according to your measurements, but I've mixed & matched many RS sticks over the years and never had this problem.
 
Chuff

Paul
The rubber on your gear lever has perished and no longer has the strength to raise the lever vertically as it should for 1-2-3-4 gear changes. Hopefully if you lift the lever vertically by hand as you change gear it might work ok.

Hi Guys,
I received my RIX Engineering shift lever today and it looks to be excellent quality as I’d hoped. When I compared it with the original, the measurement down to where the forks sit over the “saddle” on the shift shaft was approx 4mm shorter so I it seems that maybe my original shifter had either worn in the nylon “ball joint” or as Phil indicated the rubber “spring” had perished and gone hard, and was allowing the shifter to sit lower than it should.

I remover the original gearbox adaptor and fitted the new RIX shift lever and everything feels great. Reverse is locked out like it should be and is easily found when the shift lever is pressed down. I haven’t driven the car yet but the shift action in gears 1,2,3 and 4 feels short and crisp. Hopefully this feels the same when I drive the car tomorrow.

I’d just like to thank everyone once again for their help. The knowledge and assistance offered by members of this forum is much appreciated and it’s great to share a common interest with such great people.

Hi Griezy. I've never seen a clip like that before because I've only ever used Type E gearboxes fitted to Aus Escorts, or Type 9 five speed gearboxes that conveniently bolt up to Escort bellhousings. That clip is for a Type 2 or 3 gearbox, which I have no experience with.