To my understanding it is quite OK to split the TX (transmit) NMEA from EZ-Guide 500 to both the BT-Dongle and Hagie 2100. But trying to connect two other RX -> trimble EZ-Guide 500 would make a mess.
For the NTRIP client you can also use the phone built in GPS position. At least with Android and Lefebure NTRIP client you can go that way. Most likely with IPhone also? 

Enclosed is a pinout of EZ-Guide 500 D9sub connector "Port A". You can of course use the other port with the round connector "port B" but is it kind of expensive cable  to buy.

With a simple splitter you can have from D9sub at same time CMR in (pin RX) NMEA out (pin TX) radar pulse out and external switch input for a "paint" switch.
You can find ready made splitters cables or make your own.
Screw type connectors make it a bit easier: like https://www.ebay.com/itm/355819086324

For RTK corrections it has to be CMR for EZ-Guide 500. RTCM does not work for RTK with this old display. It works on External RTCM for DGPS (=same as WAAS...) but if there is more than 12 satellites in the correction stream the display will go to boot loop... So no use for that.

EZ-Guide 500 on RTK is a good old reliable robust receiver. And if you can find a EZ-Remote "joystick" a handle with buttons it is very useful. EZ-Remote connects to the same CAN line where the EZ-Steer and maybe also EZ-Boom is. 

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