I have a parameter of type Extended Choice Parameter and I have that configured to be a check box with multiple selections. After the job runs you can see the job's parameters and the value seems to be a comma separated string. However, when I use Build Periodically With Parameters and I use the syntax like this

MY_CHECKBOX_PARAM=checkValueTwo,checkValueFour

for example, the MY_CHECKBOX_PARAM value is just empty when you inspect the job later. But if you just do

MY_CHECKBOX_PARAM=checkValueTwo

and inspect the job's param values later you can see that it's value is correctly checkValueTwo and not empty. I've experimented with several other guesses at syntax and all result in empty values:

MY_CHECKBOX_PARAM=checkValueTwo,checkValueFour;
MY_CHECKBOX_PARAM="checkValueTwo,checkValueFour"
MY_CHECKBOX_PARAM='checkValueTwo,checkValueFour'