"Require that every lightbulb have/has"

Solution 1:

It has to be have there: one requires that something else have something. That makes your sentence:

Many people require that every lightbulb within a house have a switch.

To say has sounds ungrammatical to my North American ear:

Many people require that every lightbulb within a house *has a switch.

I mean, gee, if you’re going to go to all the trouble to use require that, one would hope that you would bother to get the grammar right. It is like fingernails on a chalkboard, or subject–verb disagreement.

Another possibility is to use some demanding modal, like shall or should or must, but that sounds like legalese. It would be more natural to write:

Many people require every lightbulb in a house to have a switch.

Notice I also reduced within to in. No reason to use within there.

Solution 2:

The infinitive form is have not has.

The structure of your sentence is of the form:

{propositional part of the predicate}{argument of predicate about the state being proposed}.

The sentence structure allows you a choice of either describing the state with an infinitive phrase, or with an existential phrase.

• {proposition}{infinitive state}.
• {proposition}{existential state}.

IOW,

• {proposition}{universal argument}.
• {proposition}{existential argument}.

Or, let me propose the polymorphic function,

• UniversalProposition predicate(Universal arg)
• ExistentialProposition predicate(Existential arg)

The use of to as an entry-point into the state restricts you to describe the state as an infinitive.

• State law requires her to {have auto-insurance} to drive.
• State law requires her to {have auto-insurance} before driving.

Implied/dropped to.

• State law requires her {have auto-insurance} before driving.
• She lets her children {eat non-kosher food}.

The propositional verb is requires, which is subjected to plurality rules. The infinitive argument is not subjected to plurality rules.

You could choose to describe the state as an existential state:

• State law requires that every driver {is covered by auto-insurance}.
• State law required that every driver {was covered by auto-insurance}.
• State law requires that all drivers {are covered by auto-insurance}.
• School regulation requires that a student {eats breakfast before lunch}.
• School regulation requires that every student {eats breakfast before lunch}.

Or as an infinitive:

• State laws require that every driver {have auto-insurance}.
• State laws require that a driver {have auto-insurance}.
• State laws required that a driver {have auto-insurance}.
• School regulation requires that every student {eat breakfast} before having lunch.
• School regulation requires that a student {eat breakfast} before having lunch.

Which form of argument to use

Therefore, it appears as our choice to either

• make a statement specific to the existential case
• or attempt a grandiose declaration of infinite and/or universal truth

Therefore, if one is to speak logically, the structure of their sentences should flow syllogistically,

• Universal declaration: School regulation accepts that students are precious and therefore requires that a student {eat breakfast} before having lunch.
• Specific existence: School regulation accepts that their students are precious and therefore requires that a student {eats breakfast} before having lunch.

However, this is also logical: Universal predicate, existential instance argument.

School regulation accepts that students are precious and therefore requires that a student {eats breakfast} before having lunch.

But the following is not syllogistically fluent: Instance predicate, universal argument.

School regulation accepts that their students are precious and therefore requires that a student {eat breakfast} before having lunch.

You see, an instance consumer can partake of a universal resource. OTOH, a universal consumer cannot normally partake of an instance resource. Look at the following and see which is logical and which is ironic:

• I live in my house by the ocean in Maine every day (universal), and therefore I could visit the beach by that house every Tuesday (instance).
• I drive to my house by the ocean in Maine from Vermont every Tuesday (instance), and therefore I could visit the beach of that house every day (universal).