Not much activity on the sites so far. But if you managed to hear those TG1081885 calls it was on ch129 on site 35.6 and you where monitoring a control channel frequency. When it says that TG and private calls use both slot 1 and slot 2 you are monitoring a voice channel as the control channel always use slot 2 (?) which is an even numbered channel.
To me it made more sense with site numbers if I set the TIIIareaLength to 2 in the DSDPlus.networks file as it match with what the radio techs called it when they managed the system, but depends of how the system admin have set it up.
It doesn't send any adjacent site info, what sites that radios should roam to if they loose coverage, or DCC color code. So this is the first site they built, or the system only has one site but the site number indicates that several sites are planned.
In the TIII system I monitored it looked like this when I had DSDPlus on site 12's control channel:
2018/05/22 22:58:32 Current network: L13 Net13
2018/05/22 22:58:32 Current site: L13-1.12
2018/05/22 22:58:32 DCC=3 L13-1.12 neighbor: Site L13-1.13; CC=532 423.306250
2018/05/22 22:58:32 DCC=3 L13-1.12 neighbor: Site L13-1.15; CC=558 423.468750
2018/05/22 22:58:33 DCC=3 L13-1.12 neighbor: Site L13-1.16; CC=546 423.393750
2018/05/22 22:58:34 DCC=3 L13-1.12 neighbor: Site L13-1.17; CC=506 423.143750
It only seem to be one control channel frequency and one voice channel frequency that are in use so far in your system.
The voice channel are the ch129 and also ch130. You have the frequency for that and you have the frequency of the control channel.
Use the LSN/LCN calculator to see what channel number the control channel has, and you already know the voice channels number and frequency, and enter the findings in the DSDPlus.frequencies file and when that are correct it will track and monitor the calls.
TIII, 13, 1.12, 543, 423.38125, 413.38125, 0 #OK
TIII, 13, 1.12, 544, 423.38125, 413.38125, 0 #OK
TIII, 13, 1.13, 511, 423.18125, 413.18125, 0 #
TIII, 13, 1.13, 512, 423.18125, 413.18125, 0 #
LCN to Frequency calculator for DMR TIII | RadioReference.com Forums
It looks like you only have one control channel. The frequency where you hear TG and private calls are the only voice channel in use. You mention two TIII systems but only one control channel have been found. Do you get different system id from them or perhaps the one without control channel are actually just the voice channels to the first system?
/Ubbe