How do I install a "Mister Bean lock" that's effective and prevents water intrusion?

Nothing says style like having external locks on your truck, but I've committed worse sins. I'm not going to comment on the legalities, external locks are common on delivery vans so I'm assuming it's not an issue. I would make sure both sides are unlocked when you drive to make sure you can be rescued in an emergency!

As for what kind of lock I'd suggest a slide bolt lock (aka a pad bolt lock) just like in the video. Hasp and staple locks have parts that swing and would bang around as you drive, and could possibly scrape other cars if you get close enough. As for how to attach them there's the easy way, and the harder way. The harder but stronger way is to open up the door and use carriage bolts, which are completely smooth with a square neck which anchors into a square hole in the lock plate. You then tighten the nut from behind. I would use some big washers or better yet a bit of metal plate on the backside of the door to spread the load if someone does decide to pry your door open. You'll want to make sure the length of the bolts is as short as you can get away with to prevent them from interfering with the window mechanism. I'd also suggest using threadlocker or locking nuts as rattling will tend to loosen things and you really only want to have to do this once!

The easier way is to use some sort of metal screw, preferably with a security head of some kind, again short so it doesn't interfere with anything. You would likely need to use these on the part of the lock going into the pillar, unless your truck would allow access from behind.

As for water ingress I'd just use some exterior silicone around the holes.

You could think about getting a pair of working doors from a salvage yard and attaching them instead. Depending on the make and model this may be a simple and cheap option.