First off, need to point out that there are TWO different "Flavors" of the 150 Watt HPS Lamp + Ballast.
One Lamp is a 55 Volt Lamp, the other one is 100 Volt.
S55 is the ANSI designation for the 55 Volt version of the 150 Watt HPS Lamp. It has a "Normal" Medium Base - such as the typical Medium base used on common type "A" Incandescent Lamps of 25-150 Watt power ratings @ 120-130VAC.
S56 is the ANSI designation for the 100 Volt version of the 150 Watt HPS Lamp. It has the "larger" Mogul Base - typical of most HID Lamps of >100 Watts power.
If the Ballast you are driving the Lamp with is not properly matched per the Lamp's Voltage rating (sounds like this may be the case), then the Lamp will suffer from continuous cycling (on-off-on-off-on-off...).
Also, does the non-functioning HPS Lamp work properly in another fixture? Verify this ASAP to rule out a bad Lamp.
The type of Pulse Ignitor is also critical for correct operation. Some Ignitors are intended to be used with 55 Volt Lamps, others are intended for 100 Volt Lamps - still others are meant for use on Metal Halide Lamps, being of Pulse-Start types.
The fact that Smoke is being let out of the Windings makes me wonder if the Ballast is connected properly, or if there's a failed section of a winding.
Could also be a poor contact point.
Anyhow, check these items, then reply back ASAP:
[*] Is the Lamp's Base Medium or Mogul;
[*] Is the Ballast a CWA type (Constant-Wattage Autotransformer), or Straight Linear-Reactor;
[*] Is the Capacitor connected properly, or if unsure, does it connect to the Lamp or connect to the input;
[*] Is the Ignitor connected properly + the right one;
[*] With the Ignitor disconnected, what is the output voltage found at the Lamp Socket;
[*] How many Line inputs does the Ballast have.
If the Lamp socket can fit a Medium based Lamp, will a 150 Watt Incandescent Lamp work in place of the HPS Lamp? (disconnect the Ignitor prior to this test).
If you need to verify proper connections or references, there are many HID Schematics at the Technical Reference section here at ECN.
Goto that area, select the "Menu For Technical Reference Section", then check the drawings listed for your type of Ballast.
Let me know if you are unsure of anything listed here, along with which Schematics to check, and I'll add more information for you - along with including links to the Schematics for verification.
Let us know whazzup ASAP!