Interesting...hmmm.....not sure that applies here, but thanks for that info.
Since it is your icon that doesn't have the GB icon, it means that all your existing GBs are either at their maximum level (no open levels, even if you have the BPs to open the next one if you wanted), or any of your GBs with an open level is not connected to a road. If you have an existing GB with an open level (that you should be able to contribute to), and you for some reason can't contribute to it, then contact in-game support. I get this phenomenon all the time because I self-level and my donations frequently outrun my available BPs.
There are two ways to check this. One is to hover over each GB in your city and see if they all say "Maximum level". Or, go to the GB tab in your inventory and see if all the GBs with the green checkmark (meaning they are currently built in your city) have 10/10, 11/11, or any info like that where the numbers are the same. If either case is true, then you don't have a GB with an "open level". If any don't say "maximum level", or the first number is lower than the second, check to see that they're still connected to the Town Hall by roads. If they are connected, and they don't say "maximum level" or have differing numbers, then contact support to see what is going on.
Any time you have at least one GB that is connected to the Town Hall by roads and has an open level, you should see that GB icon.