My saga continues. i have an Intel NUC, BXNUC10I7FNK1, connected through a KVM switch to an LG 24" 4k monitor. The other computer on the switch is a first-gen ASUS chromebox, reflashed to run Linux. The ASUS box runs fine, without issues. It's on Debian Buster. THe NUC is running Debian Sid, because it needs the newer kernel, and shiny is fun. During boot, the monitor shows "Signal not detected" and eventually goes to power-save mode. I can watch the disk activity light on the NUC, and enter my LVM password, then my username and password, all in the blind, and get a normal desktop. If I connect the NUC to the monitor directly, I get the normal boot display, albeit at 3480x2160x60. The monitor requires a 30Hz refresh rate, so the display is flaky and drops out now and then, but it's usable just for booting. Once the Xfce desktop comes up, all is well in either configuration. I've poked around in grub, BIOS, and kernel command line options, without success. My search foo appears to be weak on this subject, because I've been searching for several days. Does anyone have a pointer to where to look for fixes? The Intel forum has been of zero help. Likewise, the KVM switch manufacturer. I'm getting a new switch sent, but it will take awhile, and I'm frankly skeptical about the switch I have being faulty.

You need a kvm that has the faux video in the settings that you require I'd assume.

On problem ones I move the computer with issues to the first/default kvm side.

Guess you could play with kms. KMS tries to make a seamless transition between boot and gui in terms of video settings.

Does the NUC have the same issues if you switch ports on the KVM?
Another option is to try a different display manager to login to the desktop with. I think ldm the default for XFCE, so try sddm, lightdm, or gdm3 and see if if one of them shows up.

OK. Lots more reading for that. But I have more time than money, at least I hope so.

I've given up on this. My solution remains to connect the two computers to separate inputs on the monitor, and switch the keyboard/mouse with a USB switch. It's less convenient, but it works, and I'm tired of spending the time dealing with it. Thanks for the suggestions.

The cause of the problem is that the NUC isn't capable of 4k video through HDMI. I bought a Thunderbolt3->Displayport cable and that works fine with 4k video at 60Hz. The KVM switch doesn't work, obviously, but at least I get the proper video to the monitor.