That’s a nice, straight and original single speed Trusty. The slot in the side of the left hand handlebar is for the brake lever rod- when the Safety Reverse was fitted (an optional extra) the lever to engage the reverse gear fitted underneath the left hand handlebar in the position that the brake lever was normally fitted, so the brake lever was re-positioned to the side of the handlebar and it’s actuating rod went inside the tube through the slot.
Many of the single speed tractors from the late 40’s were neither fitted with a brake or a Safety Reverse but still appeared with a slot in the side of the handlebar. It appears that a whole batch was made like this, so please don’t go searching for gearboxes or brakes because the probability is that it was never fitted with either.
Did you ever get the dog clutches to engage smoothly? Trusty clutch springs are available from the club shop if you need them.