Sometimes the rules for gurps can be a bit confusing, and since you can customize gurps precisely the way you want it, there are many ways to do what you want.

Dual wielding is no exception in this case. The many options in dual wielding in gurps 4e gives you a wide variety of options to experience the rogue wielding 2 blades or the gunman with 2 revolvers.

There is 2 important advantages that have both pro and cons.

Ambidexterity, the pro: Ambidexterity basicly removes most penalties when you use 2 weapons. Though the advantage is tempting to take the con is that ambidexterity is actually pretty rare and thus somewhat unrealistic. Though at 5 points I don't see any reason not to take it.

Extra Attack, the pro: This basicly gives you an extra attack for free. No penalties except that you get -4 on your offhand attack. Combined with ambidexterity this is a sure thing. Giving you 2 attacks and 2 possibilities to hit your target at no penalties. The con is that the extra attack is a 25 point advantage and in low point campaigns the 25 points could easily be spend on extra attack damage, better skill or a talent raising the skill points.

On the attack side there is 2 possibilities, you can either perform the all out attack leaving you defenseless. You want to do this when attacking small targets that you almost certainly can kill in one hit or that is mostly harmless towards the level of your passive armor.

Besides that you can perform a Dual weapon attack, it gives you 2 attacks one at -4 and one at -8 or also at -4 in case you spend the 5 points on ambidexterity this is where on a low level campaigns you would want to spend the 25 points on skills instead of the extra attack since you should easily be able to give your self a few points to compensate for the -4 skill penalty.

If we spend the 50 points buying Ambidexterity for 5pts, Extra attack for 25 and spending 20 for the Short Sword Attack skills. Where would that get us ? Assuming we have ST: 10 DX: 10 and 4 pts already in our Short Sword skill. That would place our attack skill at 16. Giving us a one hand attack at 16 and offhand at 16, then we could go all out attack and give us an extra attack at 16 and then make a rapid strike with the offhand at -6 so effective skill at 10, though no defense, we would have 3 attacks with 98.1% chance of landing a blow and 1 attack with 50%, 3 of the attacks also have a 10% chance of critical strike, leaving the opponent defenseless at worst, expecting to deal at least 2 x 1d-2 damage in a turn, with a max of 4x1d-2 and a minimum of 0x1d-2. Of cause this is highly ineffective against heavy armored targets where a 2 handed weapon is more effective.