At the age of 8, if he has already demonstrated that he is capable of practising regularly then I personally wouldn't stop him.
I have twins, who both started piano age 4. My DS then added cornet (age 5) and violin (age 6). He worked hard at all of them, only dropped piano when our lovely piano teacher moved away, and is now (age 11) grade 4 on cornet and grade 3 violin.
It is very possible to play multiple instruments well.
In a note of caution however, my daughter has started and given up many instruments. My husband has tried to prevent the giving up every single time, most recently when she wanted to drop guitar for flute. She was allowed to have both instruments, but never underestimate the determination of a child being made to play an instrument they don't want to anymore. It becomes an absolute battleground on a daily basis.
I have learnt my lesson from that, and I refuse to try to make a child play an instrument they don't want to.
Re teachers, I can't comment on who might be available in your area, but most music teacher like to see beginners little and often to correct mistakes before they become habits.
DS(8) has been badgering for music lessons for a while. In a vain effort to stall him we insisted he played recorder for a year in the school club to prove he would persevere and do the required practise- he did At a music taster afternoon he fell in love with the oboe, he just stood for ages like that listening. Roll on last September and we now have an oboe and weekly lessons. He is diligent about his practise, finds parts of it very easy due to his fanatical recorder playing and apart from his appalling record with the reeds we are really pleased the neighbours less so! He still plays the recorder as well and it seems he has taught himself to read music (a skill that still evades me to this day ) On a day out in town I recklessly took him in the music shop- with hindsight this was A Big Mistake! Over the years he has mentioned playing the guitar but we glossed over this for family reasons (these are no longer relevant) In the music shop I found him mesmerised by the electric guitars and professing a deep desire to play. He is still on about it now. So when is a good time to add another instrument? He goes to middle school next year which seemed a logical time to me. He is less convinced. Ideally we ant him to concentrate and achieve a reasonable level on the oboe first, but we do not really have the argument that he will neglect the oboe for the guitar as he has proved himself to be committed to all we have asked of him. Also does anybody know if we could find him a teacher who would be prepared to see him every 3-4 weeks? I thought that if he had a private lesson, was set a certain amount to work on and then returned when it was completed we could keep it more lighthearted and it would be less likely to conflict with the oboe. I'm not sure if teachers would be prepared to do this or if it is inappropriate at his age <disclaimer- fantastically unmusical mother> I want to do the best for him but sadly my recorder playing ground to a halt at "Three blind mice"