Hi Richard,
do not buy a new module till it is 100% sure that that is the fault. Dealers like to change modules.
I would suggest you ask the same question on these 2 boards in the U.K., where most of the E32 drivers are members. They also have a good knowledge and might even be able to swop their trans modules with you for a test if you tell them where you live. They also have some members which might have the right module for you for small money.
But you have to mention the exact month and year of production, and also the number of the trans module. The trans module has the number on a big sticker on it. The month and year of production you will find on my website below under VIN decoder, where you just have to type in the last 7 digits of your VIN.
Links
http://www.bmw7resource.co.uk/
http://www.the7seriesregister.co.uk/
It is right that the gear mode should be indicated in the dash, otherwise the
electronic switch below the gear lever might be defective/dirty. You can see this switch of you go to my website below and look for the link to Jon Evans (evansweb) from the U.K.
One the 7 resource and on the 7 register they also have a diagnosis tool which they usually use to diagnose the member cars on the meetings they have. But maybe someone lives close to you and can help you.