What do I need to close an electrical circuit for a certain amount of time
I see Steven and Russell have given you good answers.  The old 555 timer will certainly work given the specs you provided, and that's the way to go if you are sure this is precisely the problem you want to solve.  By the way, as Steven mentioned, the general name for this type of timing block is monostable multivibrator, but it is more popularly known as a one shot.  There are also dedicated one shot chips that should be simpler to hook up since they are more targeted.  The 74x122 is one example, although I haven't checked whether it supports times as long as 30 seconds.

However, the real purpose of this answer is to point out a totally different approach, which is to use a microcontroller.  Even the smallest, simplest, cheapest micro can do this, like the PIC 10F200.  If you're not already familiar with micros, then this will take a lot more to get going.  However, if you are truly interested in electronics and envision doing other projects, then learning about micros is really useful.  In fact I'd say it is essential.  Nowadays microcontrollers are indispensible electronic components along with resistors, capacitors, and transistors.  If this were a commercial product, I think most professional electrical engineers would use a micro, not a analog timing chip.

The advantages of a micro are:

Smaller.  The PIC 10F200 comes in a SOT-23 package.  All it needs is a bypass cap.  It can be configured to have internal pullups on some pins, so a mechanical switch can often be connected without additional parts.

Probably at least as cheap after considering production costs.

More accurate and stable.  Even on a bad day, the oscillator in the PIC 10F200 is good to a few percent.  You're not going to find analog parts that accurate, especially the capacitor, without significant cost.  Over the full temperature range, analog parts will be even worse.

More flexible.  Right now the spec is to simply act like a one shot.  Might the requirements change a bit before the product goes to market?  What happens when a customer wants a blinking light to indicate the output will go off within 5 seconds?  What about different versions that do 10, 20, and 60 second on times?  You probably say that won't happen, but in the real world this sort of thing happens a lot.  Some sales guy promises a 60 second version to a customer, and all of a sudden you have to make a new variant.  With a micro this is a minor firmware change.  With a analog solution parts would have to be changed, and then you have to worry about stability at long times.



None of these points may apply to your instance right now, and the analog solution may be perfectly fine for your case.  However, I want you to at least be aware that there are other ways.