Before you try to start this, make sure the fuel tank is clean and contains fresh fuel. The fuel lines need to be in good condition - that is soft - with out cracks. Old fuel filters should not be used.

The opposed twin is equipped with the easy spin starting that allows the starter to turn the engine. With this system, the intake valve is open about 1/100 of an inch for part of the compression cycle. If I understand your description, I believe the basic engine is ok. Prime the engine with a teaspoon of fresh fuel - down the carburetor throat. See if the engine will start.

Fuel pump hoses are hooked correctly.
Have you replaced the engine valves? If yes, did you have a small engine shop grind the the valve seats and set the valve stem length to the proper length?
These engines do not have adjustable valves (in the usual manner), instead.......the valve stem must be precision ground (machine shop procedure) to fit each valve to its specific position in the engine. After fitting each valve, the valve must be kept in the position it was set for.
If the valves were indiscriminately swapped from one cylinder to the other.....an intake valve may be too long for its new cylinder location.
Same could be said if a new valve was installed but never fitted properly to its location.
The type number 0133 indicates this engine has breaker points ignition.
Incorrect points gap adjustment will have a dramatic effect on spark quality.
Are you using the Briggs service manual for your work?

Thank you for the replies.

@bluemower
I'll try the fuel down the cab trick. Fuel flow is working it seems, and I can tell it's intaking some into the carb, as the level is going down.

@mownie

The valves were not messed with other than I removed some carbon from around there when I replaced the head gasket (and I scraped the pistons clear of same), however I cannot speak to what was done before I bought it. I seem to recall the guy said his father had removed it to work on a leak, or clogged intake (there was lot of grass in there in the shroud). The heads were kind of loose I noticed.

The problem with this motor, was that I could never get the flywheel off for a complete look underneath. I had to use an impact wrench to get the nut off, it was rusted, so I replaced that with a new. Tried all manner of pullers though, and none of them would budge the flywheel one iota, they just bent the bolts. The pin did not look sheared. I broke a fin trying to get the flywheel off and so installed new heads from a similar model, they'd only been used 4 hours, from a twin which burnt up because it's oil splasher fell off.

I do not have the overhaul and service manual unfortunately. Just one I downloaded from the Briggs site, for electrical.

Thanks, Robert

The forum has an e-mail facility. E-mail me for a PDF manual.

Could be the slow cranking speed is the cause of the weak spark right now. I was just looking through the manual I do have Mownie, and I don't see where my engine has breaker points? It should per the model number, but does not have any, Just the Magnetron coil with two plug wires coming out and a single black wire. I checked on the engine where the breaker points should be, but there's no indication any were ever mounted, no holes there, no plunger? The coil looks like a Magnetron composite. I will check for stuck float needle, that's possible after sitting up all this time. Will pour some gas in the plug hole see if it fires briefly per the troubleshooting tip there, to isolate this dry plug condition.

Thanks for the replies.

Well, slow cranking speed will definitely reduce the energy of the spark.
Since the actual "pedigree" of the engine you acquired from e-bay is unknown.........the engine may not actually be "type 0133".
Parts from unknown sources could have been put together from a number of basket case, failed engines. The fan housing where the engine ID is stamped might have come from an older engine.........and placed on a newer engine.
In which case.......you are just going to have to go with the physical evidence (lack of breaker points) to guess that the engine is actually later than type 0500 which the manual states was the cutoff point for "points".
Walt Conner has built and repaired many of the Opposed Twins and may have some insight on your issues or at least an answer to the breaker points incongruity.
Walt Conner...........HELP!

The heat and mosquitos have made working on the thing a problem until recently. I pulled the plugs today and did a finger compression test. With carb facing me, the cylinder on the left has good suction, and also compression during a manual turn through (pulling finger tip in, or blowing it out)...the cylinder on the right is very 'flat'. I felt far less than on the other side. I wonder if they swapped the valves on that side perhaps, might explain the discrepancy. Dang.