Sounds like he's having mild seizures perhaps, but it might be tremors. Could be acidosis, for example if he'd gotten into a lot of pellets, or a lot of grains, or just more than what his body is used to, or has suffered prolonged over-exposure to overly rich foods. You giving him the same...
If I'm reading it right, your old dog had seizures the night before your goat did? If that's right, is there possibly a contaminated water source or food item both may have consumed or other toxins they may have been exposed to?
Best wishes.