Inspection of the eardrum may sometimes demonstrate subtle movements due to contraction of the tensor tympani (Cohen and Perez, 2003). Tensor tympani myoclonus causes a thumping. Another muscle, the stapedius, can also make higher pitched sounds. See this page for more. Opening or closing of the eustachian tube causes a clicking. The best way to hear "objective tinnitus" from the middle ear is simply to have an examiner with normal hearing put their ear up next to the patient. Stethoscopes favor low frequency sounds and may not be very helpful.
Supporting the idea that central reorganization is overestimated as "the" cause of tinnitus, a recent study by Wineland et al showed no changes in central connectivity of auditory cortex or other key cortical regions (Wineland et al, 2012). Considering other parts of the brain, Ueyama et al (2013) reported that there was increased fMRI activity in the bilateral rectus gyri, as well as cingulate gyri correlating with distress. Loudness was correlated with values in the thalamus, bilateral hippocampus and left caudate. In other words, the changes in the brain associated with tinnitus seem to be associated with emotional reaction (e.g. cingulate), and input systems (e.g. thalamus). There are a few areas whose role is not so obvious (e.g. caudate). This makes a more sense than the Wineland result, but of course, they were measuring different things. MRI studies related to audition or dizziness must be interpreted with great caution as the magnetic field of the MRI stimulates the inner ear, and because MRI scanners are noisy.
Atherosclerosis. With age and buildup of cholesterol and other deposits, major blood vessels close to your middle and inner ear lose some of their elasticity — the ability to flex or expand slightly with each heartbeat. That causes blood flow to become more forceful, making it easier for your ear to detect the beats. You can generally hear this type of tinnitus in both ears.