The walk to Eltz Castle from Moselkern is great, but it also deters some Burg Eltz visitors. Previously, access by public transport to Eltz from nearby Rhine and Mosel towns was possible only on weekends, and schedules were inconvenient. The #365 Regiobus, which connects to Hatzenport station on the Mosel Railway, now accommodates visitors every day - and far more generously. Note that a VRM ticket covers both the train to/from Hatzenport AND the #365 bus.
https://www.vrminfo.de/fileadmin/data/pdf/fahrplanbuecher/2022/365.pdf
To find train + bus travel schedules from St. Goar, Boppard, Cochem, or whatever base town you are using for the area, use the DB rail itinerary search page and "Burg Eltz, Wierschem" as a to/from station.