Try using single quotes instead (instead of the \" stuff). (apostrophes)
EDIT: Actually, just for good measure, and my sanity, perhaps change it to this temporarily:
$sql = "INSERT INTO thumbnails (customerID,thumbNAME,thumbDATE) VALUES('" . $_SESSION['mycustID'] . "','" . $file . "',NOW())";
Might also be a good idea to escape those variables if needed, with addslashes().