Apologies - I can sometimes not be very clear with written instructions. I think in flow charts so maybe this will be helpful. The DCS TIU only sends the TMCC Engine ID and command to the TMCC base, which in turn transmits to the engine(s).
I suspect the DCS handheld or App, is what stores the DCS engine number and the TMCC engine ID. When it sends a command to the TIU, the TIU decodes the signal and sends the instructions to the TMCC base. (I cannot find the details on how this operates, not in Barry's book as far as I can tell.)
In the App, when setting up a new engine, it asks you for the TMCC engine ID, it will then assign the next DCS engine number and enter any name you wish to call the engine. DCS handhelds may be different. Unlike DCS it does not look for the engine on the track (no return signal), you just need to put the TMCC engine in the active list.
NOTE: 1) DCS cannot change the TMCC engine ID. 2) Barry shows a way to get the DCS engine number to match the TMCC engine ID if desired. 3) @dave c. you are correct about the work around - basically the method Barry suggests. 4) just a guess - it should be possible to have a DCS engine with the same engine number as a TMCC engine ID --- BECAUSE --- DCS will assign that TMCC engine a different DCS engine number. 5) @Missabe from what you describe - you can use the method Dave C describes to move the DCS number to 21.
Hope this is clearer.