Unit about 10years old. Unit will not turn on or off from thermostat but when thermostat left on sometime, late evening 11pm + the unit fires up and works until turned off from thermostat, then will not restart till next day.
Steps I have taken to fix.
Fan works, furnace works, Ducts not blocked, Air intake OK.
1. Restarted system with basic reset instructions as per manufacturer. (No Luck)
2. Replaced old manual 2wire thermostat with Bonair 2wire electronic one.
(Unit doesn't start same as old one but not sure if I am wiring it correct.)
http://www.bonaire.com.au/lib/pdf/owners/Owner_Manual_3_Star_5312250e.pdf (ref page6)

Anyone know more about unit or how to resolve my issue.

The first thing to do is to measure voltage between the two wires attached to thermostat. If voltage is the same as that coming from both sides of low voltage transformer on secondary side then the thermostat is open and problem is in t-stat. If voltage id near zero then t-stat is closed, provided you have voltage on secondary side of transformer. If t-stat is closed then problem is in the limit switch which can be wired in series with gas valve solenoid. It sounds very much like you have a source of false heat that shuts off t-stat in daytime. Where is t-stat mounted? It must be at least 3 feet or one meter from an outside wall or source of heat such as an electric light or stove. T-stats are very sensitive and conditions may have changed over the years. Let me know what you find. DrTom4444