sqlite3 update table value doesn't update timestamp

Question

i'm using SQLite3 and i have a very simple table:

create table pulseCount (
  pulses INTEGER NOT NULL,
  timestamp DATETIME DEFAULT (1000*(strftime('%s','now')+mod(strftime('%f','now'),1)))
);

problem is, when i update the pulses value, the timestamp doesn't update as well. i read that i need a trigger to do this, but i wasn't able to make head or tails of the discussion and resolve it to something concrete or useful. and, yes, i do need to be keeping track down to the millisecond.

should be noted that, as far as i can tell, the timestamp updates on INSERT, but not on UPDATE, which is what is needed.

anyone willing to lend a hand here?

EDIT: as requested, the UPDATE command:

UPDATE pulseCount SET pulses=1;

as there's only one row, there's no need for a WHERE clause.

EDIT:

well, i managed to bash together a trigger that seems to work just fine:

CREATE TRIGGER [UpdateTimestamp]
  AFTER UPDATE ON pulseCount
  WHEN old.pulses <> new.pulses
BEGIN
  UPDATE pulseCount 
    SET timestamp = (1000*(strftime('%s','now')+mod(strftime('%f','now'),1)))
    WHERE pulses >= 0;
END

if anyone sees a problem with this, please do let me know. i don't know that the final WHERE clause is needed, but it can't hurt... although if it can save me a few milliseconds, i'd like to know.