The second tube in a 500+ is about 70 times less sensitive than the first one. More precisely, these are the sensitivities as used in GeigerLog:
first: 154 CPM/(ÁSv/h)
second: 2.08 CPM/(ÁSv/h)
So, at background of 20 CPM as seen by first, the second delivers 0.3 CPM, which is shown as zero. In 3 min you can expect 1 count.
Whether this tube is even meaningful has been a matter of much discussion in the past in several topics. You'll find one e.g. here: