Star down under.:
David, I seem to have led you astray a little. The 1800s were the last of the Red Rattlers, by 1960 they would have been on borrowed time, these were AECs, photo below.The 1900s were Stainless with blue trim, some lacked the blue on the sides. These were introduced in the mid 50s. They were also AECs, but had problems with the gearbox. Photo below.
From 1959 the 2000 class superseded the 1900s. These were also AECs, fitted with SCG of Coventry four speed gearboxes. Photo below.
Your railcar must’ve been an 1800, as all other Red Rattlers would’ve been retired by 1960. Details of each individual unit would have varied as they were modified to fill their differing roles.
I fully empathise with your hazy recollections, who are you?
Not sure you led me astray, but we have certainly been at some sort of cross purposes. None of those pictures look anything like what I travelled on. They look like trains to me, whereas what I rode looked just like a single decker bus coming down the road, with an interior engine but the Crossley radiator plainly in view, no fairing of any kind. And certainly no extra carriages towed behind. The driver sat next to his engine and the passenger entry was at the front, just like a bus. You paid the man and then took your seat as he took off to all intents and purpose just as in a lorry or a bus, but with no steering wheel. 3 pedals, gear lever and handbrake, but no steering wheel. He drove with his hands in his lap except when changing gear.
If you can imagine this but without the half cab and wheels and with the entry door at the front. The engine hump was not so high probably because the whole body was set higher on the rail bogies. I was not familiar with Crossleys which is why I know for certain it was one, because how else would I have known without seeing it written across the top of the rad? I can’t find a better picture on Google, maybe the one I saw was a complete one off and rarity. 
Were you around at the time, and where were/are you? 