No matter how you phrase it, most of your relatives have no, or very little interest in genealogy, at this time.
I have paid for about a dozen tests for relatives. I tell them it will significantly help me. Even when I pay, there is still some selling of the idea. I can tell you that a very high percentage of DNA Relatives I have contacted over the years, didn't even know about the genealogy feature.
On AncestryDNA, they did it for the Ancestry Composition, which is one reason given to me by my 23andme DNA Cousins but a significant number of 23andme users did it for the Health and Traits reports.
Only contacts from FTDNA did it for Genealogy, but many, if not most also subscribe to 23andme and/or AncestryDNA.
Determine what the cousin is interested in, but getting them to pay for all of it is a significant hurdle to overcome.
You will find significantly more 4th cousins and closer by testing you and your mother on the different DNA Services than you would testing your brother. You won't find additional DNA Cousins by testing cousins, but it may help you connect to your current matches.