The red triangle with an exclamation mark means you are in recovery mode. In fact recovery is the module that should install the update, so that much is normal - not installing it is, of course, not.
"Google error" sounds like standard support line bullshit: "I don't know the answer so I'm going to blame someone else".
So, you say you bought a new HTC 10 on eBay, but almost certainly it's not "new", and it's possible that something the previous owner did is responsible for this. The first thing I'd try is to just do a factory reset, in case there's anything in the cache that's stopping it (I'm assuming, since the phone is new to you, that there's nothing on it you can't set up again - if there is you could try clearing the system cache from recovery mode: on HTC's there's a trick to get the recovery menu, I think it involved pressing power and "volume up" together while on the recovery screen. I don't know why they hide the menu).
If it still won't download after that then the next question is whether the phone has been modified by a previous owner? If it has then that might interfere with the update. The fact that it's got the standard recovery suggests it might not have been, but it could also have been modified and then not properly restored to stock. In the bootloader screen (which you enter by rebooting while pressing "volume down") does it say "locked", "unlocked" or "relocked" at the top? And does it say "S-On" or "S-Off"? An unmodified phone should say "locked" and "S-On" (though it's possible for someone who genuinely knows what they are doing to reset it to that state if they had it S-Off).
A web search suggests that software version 2.41.605.12 would be for a Verizon phone: is that what you have bought? If so you could try Verizon's
Software Update Assistant tool. I was hoping that their
support page would just have a direct link to the software package, but hey ho. If that doesn't work let us know and we'll see whether we can find the upgrade package on the web somewhere (note that using that will also reset the phone, so I'd make sure anything important has been backed up).
