This sounded off to me, so I checked. Of all the vaccines listed on the CDC website, seizures are only listed as a possible complication for five of them, and never in the "1 in 1000" range you quoted. (Quoted from www.CDC.gov)
DTaP: Seizure (jerking or staring) (about 1 child out of 14,000)
Japanese encephalitis: Seizures or other serious nervous system problems (between 1 in 50,000 and 1 in a million).
MMR: Seizure (jerking or staring) caused by fever (about 1 out of 3,000 doses)
MMRV: Seizure caused by fever (about 1 child in 1,250 who get MMRV), usually 5-12 days after the first dose. They happen less often when MMR and varicella vaccines are given at the same visit as separate shots (about 1 child in 2,500 who get these two vaccines), and rarely after a 2nd dose of MMRV.
Chicken pox: Seizure (jerking or staring) caused by fever (very rare).
OP: Good luck with your research. Like others have mentioned, be sure you're getting information from good, reputable sources.