Hello Z X,
I haven't tried all the possibilities, but if SUM(VAR1=""), SUM(VAR2="") are trying to find rows that have column VAR1 empty string and column VAR2 empty string, following SQL query seems to work :
SELECT COUNT(*) as CNT_TOT, (SELECT count(VAR1) from table_name where VAR1 = '""') as CNT1_MISSING, (SELECT count(VAR2) from table_name where VAR2='""') as CNT2_MISSING .
Let me know if this is your intention.