It depends what you mean by 'across the body', as that can mean different things to different people. The actual grain runs in the same orientation as the neck. If you have flame maple figuring, then that actually runs across the grain, and will normally be orientated from top to bottom i.e. at 90° to the neck. So you should still really sand in the direction of the grain, not the figuring. https://www.sweetwater.com/insync/flame-maple/
But really, the veneer doesn't need any sanding to start with. Yes, check for glue spots,and use a suitable solvent to remove any. In the middle along the veneer join and around the edges by the binding are the typical locations, but an occasional glue-covered hand in the factory can leave random spots, so check all over the top using turps or metho. Any light spots are where the glue stops the wood taking up the liquid (and will do the same for stain). You can use water, but it will raise the grain, and whilst it's good to do that once (and lightly sand off the loose grain), you don't want to keep doing it with veneer.
If you are doing a dark colour first to accent.'pop' any figuring, then you'll need to sand back to expose some unstained veneer again. But be very gentle as the veneer is only 0.5-0.6mm thick. P400 or higher for sanding, and then lightly rough the surface with P240. then add the main stain. If water-based this will raise ant remaining loose grain, so just do a 'drag sand' with P400 to pull those loose fibres away. Then you're ready to apply finish to the veneer.
Don't sand too often with TruOil as each layer is very thin and you're likely to remove more finish than you've applied if not careful. As Dacious has said, the first few coats will simply sink into the veneer. I'd be tempted to apply 10 coats or so before doing any sanding. It's heartbreaking to sand through the TruOil and take finish off the veneer, as it's really hard to touch up once it's got TruOil on. But use your eyes and some common sense and if it's not sinking in much then maybe do the first sand a couple of coats sooner. If you aren't going for a natural/satin look and want it smooth and glossy, the whole idea is to build up enough layers so you can sand the finish flat and smooth and then polish it. Almost all finishes will simply follow the contours of the wood, so it won't get smoother as you add more layers. So you've got the options of either trying to sand it flatter every few applications, or just lightly sand occasionally to remove obvious hairs or dust particles and do the bulk of the sanding work after 30-40 applications or so. But there is far more sand-through risk with the first method, especially on a guitar with a curved top like the ES-1. It's very easy to sand through on the top of the small convex curves (having done it myself).