Rec/Play head part no. 5378306000
You can order it new (if they have one, good luck with used) from parts department at teac. com...They're in California...I recently tried to order a capstan belt from them and they gave me a link for the Canadian Division who then said they had to order it from California...go figure! I ended up on ebay for that one as it would have taken 6-8 weeks for it otherwise. Maybe you have a better source in Europe. I hope so!
Hope you get recording on it soon, I may be looking at the same problem with my own 388. Oh, and I'm sure you have the manual but if not just google it and the pdf. is available.