Solo Connect has used different make and model modems over the years, though all modems to date have been 3rd party modems where LiveU does not have direct control over things like what the LED lights on the modem do or indicate.
Most recently, some kits include a Novatel 730L that may say "Verizon Wireless" on the modem. These modems look overall similar to the Inseego USB800 sometimes also used. However, the light on the Novatel 730L will illuminate orange, whereas the light on the USB800 will illuminate green. This is expected behavior! and does not indicate a problem.
The Novatel and Inseego modems are based on some of the same platform (Novatel later sold their modem business to Inseego), however they run different firmwares and interact with the sim cards that LiveU uses differently. Thus, the Novatel lights up orange, even when working perfectly normally.
The best indication of an active connection is on the unit's own screen, under Connections. A green icon in the row for that modem indicates the modem is connected and reaching the public internet.
Here is the Inseego USB800, when connected and working:
And here is the Novatel 730L when connected and working normally: