Bus from Kannon pedestrian tunnel

Aloha! We are planning to walk thru the Kannon pedestrian tunnel from Shimonoseki to KitaKyushu. Several articles I read say that there is a bus to Moji station from the tunnel exit, but I cannot find any specific information or timetables. So I am trying to find out for sure if there is a bus and if not how far of a walk is the nearest train station from the exit of the tunnel. We will be doing the walk on a weekday.
Thanks!

Can't help you with buses but it was a pleasant easy 30 minutes coastal walk from Mojiko Station to Kyushu side of the pedestrian tunnel as there is no steep path. Not many pedestrians even on a Saturday morning. Different story at Karato Market in Shimonoseki as it was packed with people buying food to eat.

Thank you!

Wait! That tunnel name is not "Kan(n)on", "Kan(m)on".
This Kan means Shimoseki(下関)'s "seki(関)" of kanji, Mon also Moji(門司)'s "mo(n)(門)".

Anyway, bus time table(時刻表 jikokuhyo) is here,
(later mentioned, also possible by Google Maps and bus company web in EN)
"No.63 関門トンネル人道口 Kanmon tunnel jindou-guchi " stop is so.
https://www.navitime.co.jp/bus/route/00022759/%EF%BC%97%EF%BC%94%EF%BC...
https://goo.gl/maps/FPnU3NZEz362
https://goo.gl/maps/UZDVMduJud22

However, you noticed if bus route map enlarge by "+", so nearest rail station is not so far.
But this railway is not for local, one of sightseeing train, so no operated on regular weekdays.
http://www.retro-line.net/
http://www.retro-line.net/wp-content/uploads/2018/04/about_ticket_en.p...
Nearest "JR" station is "Mojiko(門司港)", about 30 min far by walk is right, but you will be getting on a bus.
https://goo.gl/maps/MK51ZgeTFhp
https://goo.gl/maps/Mj5iFYxVdik
https://jik.nishitetsu.jp/menu?lang=en
This is how to ride "Nishitetsu bus" in EN, but JP pages mentioned more.
http://www.nishitetsu.jp/en/bus/
http://www.nishitetsu.jp/bus/norikata/norikata/

Thanks you for correcting me on the proper name of the tunnel. Thank you so much for all of the information. I've only had a chance to check the forum today. I appreciate all of your assistance.