2. When two or more singular nouns or pronouns are connected by 'or' or 'nor', use a singular verb.
The book or the pen is in the drawer.
3. When a compound subject contains both a singular and a plural noun or pronoun joined by 'or' or 'nor', the verb should agree with the part of the subject that is nearer the verb.
The boy or his friends run every day.
His friends or the boy runs every day.
1) Either the king or his sons have gone there.
When composing such compound subjects yourself, it is preferable to put the plural noun/pronoun second and use a plural verb - as you have done!
2. When two or more singular nouns or pronouns are connected by 'or' or 'nor', use a singular verb.
The book or the pen is in the drawer.
The OP was no doubt aware of that.
3. When a compound subject contains both a singular and a plural noun or pronoun joined by 'or' or 'nor', the verb should agree with the part of the subject that is nearer the verb.
The boy or his friends run every day.
His friends or the boy runs every day.
1) Either the king or his sons have gone there.
You've more or less repeated the elementary points I made in my more comprehensive reply. The OP had already replied with a "thanks" which should have been sufficient to indicate that he was satisfied with the reply.