The issue is that with some extenders, they will answer the 10.10.10.23 that was reserved for the TEG, but when the extender transmits/receives from the TEG it is on a different net with an SSID of "Original-ext", say with and address range of say 10.10.11.XXX, and assigns the TEG to 10.10.11.2
If you are lucky enough to have a 2.5GHz extender that has its own pool of reservable addresses, then I think that you can reserve 10.10.10.23 in your main router for the TEG, and then in the extender reserve 10.10.11.2 for the TEG, and the assign 10.10.11.2 (or 10.10.10.23, if that option exists) in the TEG as its address on network "Original-Ext". However, not every extender does that.
All the best,
BG