So after some more testing I can say that the 2:1 divider working fine! After 3 weeks I started with this plan I finally got it working. Thanks for all the tips and advice here, especially to alec_t who was always there with real solutions, respect.
I have the coil and the new reed soldered to the side of an about 4x6cm PCB, the battery is taped to PCB with some rubber in between, and the complete unit is attached to the frame with velcro.
Now my next step is to provide a wheather protection for it. I thought of do some potting in a mold or so. I like to give the housing a suitable form to able to fix it stable to the not complete flat frame. Maybe I can 'stamp' the frame with clay to have an exact copy of the mounting location. Then I can use the 'negative' of this clay mould as a casting for the PCB and battery.
But there are some points to take care of; the 9V battery needs to replaceable, the new reed contact should 'in reach' of the magnet and the coil may not be covered to much to still be able to trigger the old reed.
Any ideas what materials to use for the molding and potting: resin, polyester,... ?