The unusable NME Sun2 Emulator 

@2:15 (ish and onwards) this is more of an anecdote than anything but I had the same exact issue back in the day on Windows 3.1 using terminal and dialing into a local BBS. I had to click the mouse or move it for the text to feed in the terminal window. Turns out I had an IRQ conflict with my modem and the mouse and it manifested itself in that behavior. Sorry, no idea what's causing it here but it's interesting to see basically the same behavior all these years later...

what OS are you running and how did you build it? The docs seem to indicate strong support for BSD operating systems - to get up and going just try it in a NetBSD virtual machine?

The first situation looks like it's deinterlacing and separating the fields into two parts of the viewport. The embedded display looks better... could the display be interrupt-driven, and it's not generating the interrupts until you prod it? Not knowing anything about SUN, I'm just spit-balling here.

Have you messed with Brad Parker’s emulator-sun-2?