Sorry, your question and code make no sense at all. You test for serial byte(1), which is the second byte in the buffer, before you even know if you have read TWO bytes.
Also, "false" means the numeric value is ZERO, all other values will return TRUE!
What are you REALLY trying to do?
What do you mean by "position 1 of serial_byte"? Do you mean the first bit of that byte? Or do you mean bit number 1, which is the second bit because bits are numbered from 0. Or do you mean something else?
byte ourByte = 0b00000010;
// read the second from the right bit (bit 1) of the byte ourByte
Serial.print("bit 1 of ourByte = ");