Know the rules by which you are playing. This may seem obvious, but I've seen it violated so many times, it definitely bears mentioning in the list of important tactics to be utilized by political neutrals.
Most organizations have certain characteristics they say are valued by the organization. One company I worked for claimed to select managers based on passion, integrity, continuous improvement, and the ability to produce results. These were partially accurate -- I would dispute the last one, where "the ability to produce results" seemed to mean the ability to hit plan regardless of the errors or mistaken assumptions plan might be based on. And I would have rejected "continuous improvement" entirely.
The point is, companies say one thing, and reality is something else. Characteristics that are stated as valuable are sometimes aspirational, representing how the company ideally would like to value its people. There are hints about what's really valued in them, but it's hardly enough to be definitive.
There are other characteristics that are not stated, but are still critical to successful. For my example company, I would add the following unstated, but highly important characteristics: Connection to important decision makers outside the company, dedication as measured by hours worked and personal sacrifices made, going along to get along, and quickness to upwardly communicate bad news. Fall short on any of these, and you may very well be out the door.
The art of managing your image within the organization becomes managing it along these dimensions. Do this well, and you're starting from a solid foundation when you get in the inevitable political battle. Do it poorly, and you're setting yourself up for difficulties.
So how do you figure out what the valued dimensions are? The primary thing to do is LISTEN. What are other employees criticized for? If you hear constant complaints about clock watching, or how quickly the parking lot clears out at five PM, or how irritating a late arriver is -- you can surmise that time committed to work is an important dimension along which you will be judged.
Should you hear people criticized for emotional or angry outbursts, then going along is probably an important characteristic. In one organization where I worked, people were criticized for not showing emotions -- specifically anger -- when challenged. You have to notice these things.
It definitely matters who's doing the criticizing -- higher level employees and obvious power players carry more weight than others.
Once you are aware of the behaviors and characteristics that are valued, it becomes your job to manage other's perceptions. Will you be the first one to the office in the morning and the last to leave at night, in an organization that values the hours you commit? If you're willing to make the sacrifice, then it can only help you.
When your reputation is openly questioned, it's important to defend yourself -- hopefully with facts. "Yes, I left early yesterday -- I needed to buy a gift for that Chinese client before I left on the trip." Don't let someone knowingly undermine you with half-truths or outright lies. If you've developed your network of relationships and alliances carefully, you'll know when these things occur. If not, you're still exposed despite doing all the right things to be in compliance with the organizational expectations.