Well. I have just tried once again to disassemble - with the same result. I was able to get to the back of the strip with all internal mechanics, springs and shafts. But not to the outer frame holding the buttons with collars.

Aren't you mixing up with the 599/598 strips, where indeed undoing the 2 screws on both sides of strip released the plastic lamp & button holder part from the cast metal housing of the mechanical part?

Again it is different on 656/657 - the lamp & button holder and the housing are both plastic, And appear to be pressed into each other - there is no visible joint line between those two parts, no movement when you try to apply some pressure between them and not single screw, tab or latch which would maintain mechanical connection between two parts.

Please send the pictures if you were able to disassemble one. Again NOT the 599/598 strips in metal housing.