find other end of ethernet cable
There are wire tracers (e.g. "fox and hound" a brand name, not affiliated, don't even own own one) or "tone and probe" more generically - you need the type with an inductive (non-contact) probe. Those inject a high frequency signal which the detector detects. But I'd start with a careful check or re-check of basement, attic and near where the telephone and or TV enter the house (I guess if the cables are "behind blank panels" rather than terminated to jacks you'd have to look inside blank panels for the other end of them, too.)