As I discussed in the other thread, more often than not, it uses LRRP, which is defined by P25. You will want to read up on the protocol, it's basically XML. You are going to want to understand the implications of this protocol. One of the reasons you will want to is the subscriber needs to receive instructions about where and how often (cadence) it should send location updates. These updates are sent on seperate channels from voice. This is more often than not what the "data" is when you are monitoring a trunked system on tools like Unitrunker or DSD+.
DSD+ (and I think SDRTrunk) naively decodes this, and this is probably going to be your best bet since it will support conventional or trunked streams. But you are more or less stuck displaying it on their map. I don't know enough about SDRtrunk to know if it will do conventional as well, but I know it can display LRRP from subscribers on a trunked system.
If you are looking to learn about LoPTT (Location on PTT) and LoRX (Location on Receive), these are proprietary to Motorola. That's what you see when you have the direct PTT with another subscriber and you can see each other's locations. You don't want to put an IMW in your core? You may be on your own developing this since you would have to reverse engineer the protocol. A tip I can provide you though is you can use something like Wireshark to decode the data in transit as long as you have a way to feed it the IQ output of the receiver. You could use this information to then pipe it to an application. You would have to decode the data string from the subscriber because the location is embedded with the voice information.... hopefully you are starting to understand why people pay the money and time for the IMW, and why there are fees for the API, etc. LoRX requires TDMA so I am sure that's a whole special beast on its own trying to reverse engineer it.
EDIT: The other point I should have made about LRRP is because the device needs instructions, you will have to get some way to trigger it initially sending the updates. Another function of the IMW in a Motorola P25 core.