I don't know of a canonical rules source for "here's how it works in D&D 3.5 when you have two characters in a single body," but I can point you to a couple of similar cases for which there are rules, from which you might draw some inspiration.

Schism

The psionic power Schism splits its user's mind in two, with each half able to take its own actions. While the source of the split mind for your character (presumably) wouldn't be the same, the description of Schism's effects sound a lot like what you're describing:

Your mind splits into two independent parts. Each part functions in complete autonomy, like two characters in one body. Your new “second mind” does not control your body physically but is free to take one standard action in each round if the action is purely mental (such as manifesting a power) in the same round you take your normal actions.

If your character concept concept is consistent with this setup, where one mind has control of the body and the other can only take mental actions, you could borrow from Schism's mechanics. Of course, since this option gives you additional actions per round, it would be a net increase in character power, so you might want to add some disadvantages to balance it out.

Fiend of Possession

The Fiend of Possession prestige class (Fiend Folio) has the ability to become incorporeal and possess characters and objects. Again, this is different from the fluff you have in mind for your character (where two characters are fused, rather than one forcibly possessing the other), but you can still borrow mechanics.

Again, this results in one of the minds being restricted to mental actions only:

While possessing an object, a fiend of possession can use any ability it has that requires no physical action, such as using a spell-like ability or telepathy. It cannot cast spells (since it can neither speak nor move), attack physically, or perform any other physical action, until it reaches a high enough level to make the possessed object perform these tasks for it.

Dvati

The Dvati (a race from the Dragon Compendium) are in some ways the opposite of your character concept (they're a single soul split into two bodies that counts as a single character), but you might want to reference them in terms of what kinds of actions might be restricted for action economy purposes.

For instance, when a Dvati character casts a spell, both halves are required to spend their action to do so (because doubling the number of spells a character can cast per round is ridiculously powerful), but they can move independently, each spending only their own action.

3rd edition

If 2e advocates that the DM makes the skill checks for the player characters, then that approach was reversed in 3e, where the default assumption is that the player makes all rolls on behalf of their character and all the instructions about making any kind of skill checks are worded that way. No explicit justification for this is given in the manuals.

Possibly, this could be linked to 3e's adoption of what it calls the core mechanic - using one simple resolution system (roll a d20, add modifiers, compare to target number) to adjudicate almost everything that happens in the game, combat or not. The intended flow is that:

1. the DM describes the situation
2. the player describes what they want their character to do
3. the DM tells them what kind of roll to make
4. the player rolls their d20 and adds their modifiers
5. the DM tells them if and how they succeed.

Complicating this by having the DM make some rolls on behalf of the character breaks this flow and may have been seen as undesirable. It also requires the DM to manage a lot more information, since they need to know the relevant statistics for the player for any rolls they need to make on their behalf. It is easier for this burden to be entirely handled by the player, as the DM already has enough to keep track of with their NPCs.

Finally, there is a general assumption in modern D&D that the point of the game is to tell a story together and that players can be trusted not to metagame - even if they know that their roll was poor and maybe they didn't spot a trap or a hidden ambusher, they play their characters without acting on that knowledge. Obviously, the truth of this assumption varies highly from table to table. I understand that in earlier versions of D&D the relationship between DM and players was traditionally somewhat more antagonistic, and the idea of essentially giving players information their characters did not have would have been much more strongly discouraged.